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11 x1 t08 06 trig equations (2012)

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Nigel Simmons
Education
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Trig Equations
Trig Equations 1 e.g.  i  cos 2  0    360 2
Trig Equations 1 e.g.  i  cos 2  0    360 2 0  2  720
Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720
Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720  
Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720 1 cos   2     60
Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720 1 2   ,360   cos   2   2  60 ,360  60   60 2  60 ,300 , 420 ,660
Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720 1 2   ,360   cos   2   2  60 ,360  60   60 2  60 ,300 , 420 ,660   30 ,150 , 210 ,330
Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720 1 2   ,360   cos   2   2  60 ,360  60   60 2  60 ,300 , 420 ,660   30 ,150 , 210 ,330 1 OR cos 2  0    360 2
Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720 1 2   ,360   cos   2   2  60 ,360  60   60 2  60 ,300 , 420 ,660   30 ,150 , 210 ,330 1 OR cos 2  0    360 2 1 2cos   1  2 2
Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720 1 2   ,360   cos   2   2  60 ,360  60   60 2  60 ,300 , 420 ,660   30 ,150 , 210 ,330 1 OR cos 2  0    360 2 1 2cos   1  2 2 3 cos   2 4 3 cos    2
Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720 1 2   ,360   cos   2   2  60 ,360  60   60 2  60 ,300 , 420 ,660   30 ,150 , 210 ,330 1 OR cos 2  0    360 2 1 Q1, Q2, Q3, Q4 2cos   1  2 2 3 cos   2 4 3 cos    2
Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720 1 2   ,360   cos   2   2  60 ,360  60   60 2  60 ,300 , 420 ,660   30 ,150 , 210 ,330 1 OR cos 2  0    360 2 1 Q1, Q2, Q3, Q4     2cos   1  2 2 3 cos   2 4 3 cos    2
Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720 1 2   ,360   cos   2   2  60 ,360  60   60 2  60 ,300 , 420 ,660   30 ,150 , 210 ,330 1 OR cos 2  0    360 2 1 Q1, Q2, Q3, Q4     2cos   1  2 2 3 cos   3 2 cos   2 4   30 3 cos    2
Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720 1 2   ,360   cos   2   2  60 ,360  60   60 2  60 ,300 , 420 ,660   30 ,150 , 210 ,330 1 OR cos 2  0    360 2 1 Q1, Q2, Q3, Q4     2cos   1  2 2 3 cos   3 2 cos   2    ,180   ,180   ,360   4   30   30 ,180  30 ,180  30 ,360  30 3 cos      30 ,150 , 210 ,330 2
 ii  4sec2 x  3tan x  5 0  x  360
 ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0
 ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0  4 tan x  1 tan x  1  0
 ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0  4 tan x  1 tan x  1  0 1 tan x   or tan x  1 4
 ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0  4 tan x  1 tan x  1  0 1 tan x   or tan x  1 4 Q2, Q4
 ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0  4 tan x  1 tan x  1  0 1 tan x   or tan x  1 4 Q2, Q4  
 ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0  4 tan x  1 tan x  1  0 1 tan x   or tan x  1 4 Q2, Q4  1  tan   4   14 2
 ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0  4 tan x  1 tan x  1  0 1 tan x   or tan x  1 4 Q2, Q4  1  tan   4   14 2 x  180   ,360   x  180  14 2,360  14 2 x  16558,34558
 ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0  4 tan x  1 tan x  1  0 1 tan x   or tan x  1 4 Q2, Q4 Q1, Q3  1  tan   4   14 2 x  180   ,360   x  180  14 2,360  14 2 x  16558,34558
 ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0  4 tan x  1 tan x  1  0 1 tan x   or tan x  1 4 Q2, Q4 Q1, Q3  1  tan     4   14 2 x  180   ,360   x  180  14 2,360  14 2 x  16558,34558
 ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0  4 tan x  1 tan x  1  0 1 tan x   or tan x  1 4 Q2, Q4 Q1, Q3  1  tan   tan   1   4   45   14 2 x  180   ,360   x  180  14 2,360  14 2 x  16558,34558
 ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0  4 tan x  1 tan x  1  0 1 tan x   or tan x  1 4 Q2, Q4 Q1, Q3  1  tan   tan   1   4   45   14 2 x   ,180   x  180   ,360   x  45 ,180  45 x  180  14 2,360  14 2 x  45 , 225 x  16558,34558
 ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0  4 tan x  1 tan x  1  0 1 tan x   or tan x  1 4 Q2, Q4 Q1, Q3  1  tan   tan   1   4   45   14 2 x   ,180   x  180   ,360   x  45 ,180  45 x  180  14 2,360  14 2 x  45 , 225 x  16558,34558 x  45 ,16558, 225 ,34558
 iii  cos 2  4cos 2   2sin 2  0    360
 iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2 
 iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2  3cos 2   sin 2 
 iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2  3cos 2   sin 2  tan 2   3 tan    3
 iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2  3cos 2   sin 2  Q1, Q2, Q3, Q4 tan 2   3 tan    3
 iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan    3
 iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60
 iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300
 iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300 (iv) cos 2  sin  , 0    360 2000 Extension 1 HSC Q2c)
 iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300 (iv) cos 2  sin  , 0    360 2000 Extension 1 HSC Q2c) 1  2 sin 2   sin 
 iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300 (iv) cos 2  sin  , 0    360 2000 Extension 1 HSC Q2c) 1  2 sin 2   sin  2 sin 2   sin   1  0
 iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300 (iv) cos 2  sin  , 0    360 2000 Extension 1 HSC Q2c) 1  2 sin 2   sin  2 sin 2   sin   1  0 2 sin   1sin   1  0
 iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300 (iv) cos 2  sin  , 0    360 2000 Extension 1 HSC Q2c) 1  2 sin 2   sin  2 sin 2   sin   1  0 2 sin   1sin   1  0 1 sin   or sin   1 2
 iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300 (iv) cos 2  sin  , 0    360 2000 Extension 1 HSC Q2c) 1  2 sin 2   sin  2 sin 2   sin   1  0 2 sin   1sin   1  0 1 sin   or sin   1 2 Q1, Q2
 iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300 (iv) cos 2  sin  , 0    360 2000 Extension 1 HSC Q2c) 1  2 sin 2   sin  2 sin 2   sin   1  0   2 sin   1sin   1  0 1 sin   or sin   1 2 Q1, Q2
 iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300 (iv) cos 2  sin  , 0    360 2000 Extension 1 HSC Q2c) 1  2 sin 2   sin  2 sin 2   sin   1  0   2 sin   1sin   1  0 1 sin   or sin   1 2 Q1, Q2   270
 iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300 (iv) cos 2  sin  , 0    360 2000 Extension 1 HSC Q2c) 1  2 sin 2   sin  2 sin 2   sin   1  0   2 sin   1sin   1  0 1 sin   or sin   1 1 2 sin   Q1, Q2   270 2   30
 iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300 (iv) cos 2  sin  , 0    360 2000 Extension 1 HSC Q2c) 1  2 sin 2   sin  2 sin 2   sin   1  0    ,180     2 sin   1sin   1  0   30 ,180  30 1   30 ,150 sin   or sin   1 1 2 sin   Q1, Q2   270 2   30
 iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300 (iv) cos 2  sin  , 0    360 2000 Extension 1 HSC Q2c) 1  2 sin 2   sin  2 sin 2   sin   1  0    ,180     2 sin   1sin   1  0   30 ,180  30 1   30 ,150 sin   or sin   1 1 2 sin   Q1, Q2   270 2   30   30 ,150 ,270
(v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a)
(v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos
(v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos 2 sin 2   2 sin  cos  0
(v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos 2 sin 2   2 sin  cos  0 2 sin  sin   cos   0
(v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos 2 sin 2   2 sin  cos  0 2 sin  sin   cos   0 sin   0 or sin   cos 
(v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos 2 sin 2   2 sin  cos  0 2 sin  sin   cos   0 sin   0 or sin   cos    0 ,180 ,360
(v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos 2 sin 2   2 sin  cos  0 2 sin  sin   cos   0 sin   0 or sin   cos    0 ,180 ,360 tan   1
(v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos 2 sin 2   2 sin  cos  0 2 sin  sin   cos   0 sin   0 or sin   cos    0 ,180 ,360 tan   1 Q1, Q3
(v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos 2 sin 2   2 sin  cos  0 2 sin  sin   cos   0 sin   0 or sin   cos    0 ,180 ,360 tan   1 Q1, Q3  
(v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos 2 sin 2   2 sin  cos  0 2 sin  sin   cos   0 sin   0 or sin   cos    0 ,180 ,360 tan   1 Q1, Q3 tan   1     45
(v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos 2 sin 2   2 sin  cos  0 2 sin  sin   cos   0 sin   0 or sin   cos    0 ,180 ,360 tan   1 Q1, Q3 tan   1     45    ,180     45 ,180  45   45 , 225
(v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos 2 sin 2   2 sin  cos  0 2 sin  sin   cos   0 sin   0 or sin   cos    0 ,180 ,360 tan   1 Q1, Q3 tan   1     45    ,180     45 ,180  45   45 , 225   0 ,45 ,180 ,225 ,360
(v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos 2 sin 2   2 sin  cos  0 2 sin  sin   cos   0 sin   0 or sin   cos    0 ,180 ,360 tan   1 Exercise 2D; Q1, Q3 2ac, 4ac, 5adgi, tan   1   9adgj, 10bdfij,   45 16, 24*    ,180     45 ,180  45   45 , 225   0 ,45 ,180 ,225 ,360

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12 x1 t01 03 integrating derivative on function (2013)
 
12 x1 t01 02 differentiating logs (2013)
12 x1 t01 02 differentiating logs (2013)12 x1 t01 02 differentiating logs (2013)
12 x1 t01 02 differentiating logs (2013)
 
12 x1 t01 01 log laws (2013)
12 x1 t01 01 log laws (2013)12 x1 t01 01 log laws (2013)
12 x1 t01 01 log laws (2013)
 
X2 t02 04 forming polynomials (2013)
X2 t02 04 forming polynomials (2013)X2 t02 04 forming polynomials (2013)
X2 t02 04 forming polynomials (2013)
 
X2 t02 03 roots & coefficients (2013)
X2 t02 03 roots & coefficients (2013)X2 t02 03 roots & coefficients (2013)
X2 t02 03 roots & coefficients (2013)
 
X2 t02 02 multiple roots (2013)
X2 t02 02 multiple roots (2013)X2 t02 02 multiple roots (2013)
X2 t02 02 multiple roots (2013)
 
X2 t02 01 factorising complex expressions (2013)
X2 t02 01 factorising complex expressions (2013)X2 t02 01 factorising complex expressions (2013)
X2 t02 01 factorising complex expressions (2013)
 
11 x1 t16 07 approximations (2013)
11 x1 t16 07 approximations (2013)11 x1 t16 07 approximations (2013)
11 x1 t16 07 approximations (2013)
 
11 x1 t16 06 derivative times function (2013)
11 x1 t16 06 derivative times function (2013)11 x1 t16 06 derivative times function (2013)
11 x1 t16 06 derivative times function (2013)
 
11 x1 t16 05 volumes (2013)
11 x1 t16 05 volumes (2013)11 x1 t16 05 volumes (2013)
11 x1 t16 05 volumes (2013)
 
11 x1 t16 04 areas (2013)
11 x1 t16 04 areas (2013)11 x1 t16 04 areas (2013)
11 x1 t16 04 areas (2013)
 
11 x1 t16 03 indefinite integral (2013)
11 x1 t16 03 indefinite integral (2013)11 x1 t16 03 indefinite integral (2013)
11 x1 t16 03 indefinite integral (2013)
 
11 x1 t16 02 definite integral (2013)
11 x1 t16 02 definite integral (2013)11 x1 t16 02 definite integral (2013)
11 x1 t16 02 definite integral (2013)
 
11 x1 t16 01 area under curve (2013)
11 x1 t16 01 area under curve (2013)11 x1 t16 01 area under curve (2013)
11 x1 t16 01 area under curve (2013)
 
X2 t01 11 nth roots of unity (2012)
X2 t01 11 nth roots of unity (2012)X2 t01 11 nth roots of unity (2012)
X2 t01 11 nth roots of unity (2012)
 
X2 t01 10 complex & trig (2013)
X2 t01 10 complex & trig (2013)X2 t01 10 complex & trig (2013)
X2 t01 10 complex & trig (2013)
 
X2 t01 09 de moivres theorem
X2 t01 09 de moivres theoremX2 t01 09 de moivres theorem
X2 t01 09 de moivres theorem
 
X2 t01 08 locus & complex nos 2 (2013)
X2 t01 08 locus & complex nos 2 (2013)X2 t01 08 locus & complex nos 2 (2013)
X2 t01 08 locus & complex nos 2 (2013)
 
X2 t01 07 locus & complex nos 1 (2013)
X2 t01 07 locus & complex nos 1 (2013)X2 t01 07 locus & complex nos 1 (2013)
X2 t01 07 locus & complex nos 1 (2013)
 

11 x1 t08 06 trig equations (2012)

  • 2. Trig Equations 1 e.g.  i  cos 2  0    360 2
  • 3. Trig Equations 1 e.g.  i  cos 2  0    360 2 0  2  720
  • 4. Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720
  • 5. Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720  
  • 6. Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720 1 cos   2     60
  • 7. Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720 1 2   ,360   cos   2   2  60 ,360  60   60 2  60 ,300 , 420 ,660
  • 8. Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720 1 2   ,360   cos   2   2  60 ,360  60   60 2  60 ,300 , 420 ,660   30 ,150 , 210 ,330
  • 9. Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720 1 2   ,360   cos   2   2  60 ,360  60   60 2  60 ,300 , 420 ,660   30 ,150 , 210 ,330 1 OR cos 2  0    360 2
  • 10. Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720 1 2   ,360   cos   2   2  60 ,360  60   60 2  60 ,300 , 420 ,660   30 ,150 , 210 ,330 1 OR cos 2  0    360 2 1 2cos   1  2 2
  • 11. Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720 1 2   ,360   cos   2   2  60 ,360  60   60 2  60 ,300 , 420 ,660   30 ,150 , 210 ,330 1 OR cos 2  0    360 2 1 2cos   1  2 2 3 cos   2 4 3 cos    2
  • 12. Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720 1 2   ,360   cos   2   2  60 ,360  60   60 2  60 ,300 , 420 ,660   30 ,150 , 210 ,330 1 OR cos 2  0    360 2 1 Q1, Q2, Q3, Q4 2cos   1  2 2 3 cos   2 4 3 cos    2
  • 13. Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720 1 2   ,360   cos   2   2  60 ,360  60   60 2  60 ,300 , 420 ,660   30 ,150 , 210 ,330 1 OR cos 2  0    360 2 1 Q1, Q2, Q3, Q4     2cos   1  2 2 3 cos   2 4 3 cos    2
  • 14. Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720 1 2   ,360   cos   2   2  60 ,360  60   60 2  60 ,300 , 420 ,660   30 ,150 , 210 ,330 1 OR cos 2  0    360 2 1 Q1, Q2, Q3, Q4     2cos   1  2 2 3 cos   3 2 cos   2 4   30 3 cos    2
  • 15. Trig Equations 1 e.g.  i  cos 2  0    360 2 Q1, Q4 0  2  720 1 2   ,360   cos   2   2  60 ,360  60   60 2  60 ,300 , 420 ,660   30 ,150 , 210 ,330 1 OR cos 2  0    360 2 1 Q1, Q2, Q3, Q4     2cos   1  2 2 3 cos   3 2 cos   2    ,180   ,180   ,360   4   30   30 ,180  30 ,180  30 ,360  30 3 cos      30 ,150 , 210 ,330 2
  • 16.  ii  4sec2 x  3tan x  5 0  x  360
  • 17.  ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0
  • 18.  ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0  4 tan x  1 tan x  1  0
  • 19.  ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0  4 tan x  1 tan x  1  0 1 tan x   or tan x  1 4
  • 20.  ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0  4 tan x  1 tan x  1  0 1 tan x   or tan x  1 4 Q2, Q4
  • 21.  ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0  4 tan x  1 tan x  1  0 1 tan x   or tan x  1 4 Q2, Q4  
  • 22.  ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0  4 tan x  1 tan x  1  0 1 tan x   or tan x  1 4 Q2, Q4  1  tan   4   14 2
  • 23.  ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0  4 tan x  1 tan x  1  0 1 tan x   or tan x  1 4 Q2, Q4  1  tan   4   14 2 x  180   ,360   x  180  14 2,360  14 2 x  16558,34558
  • 24.  ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0  4 tan x  1 tan x  1  0 1 tan x   or tan x  1 4 Q2, Q4 Q1, Q3  1  tan   4   14 2 x  180   ,360   x  180  14 2,360  14 2 x  16558,34558
  • 25.  ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0  4 tan x  1 tan x  1  0 1 tan x   or tan x  1 4 Q2, Q4 Q1, Q3  1  tan     4   14 2 x  180   ,360   x  180  14 2,360  14 2 x  16558,34558
  • 26.  ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0  4 tan x  1 tan x  1  0 1 tan x   or tan x  1 4 Q2, Q4 Q1, Q3  1  tan   tan   1   4   45   14 2 x  180   ,360   x  180  14 2,360  14 2 x  16558,34558
  • 27.  ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0  4 tan x  1 tan x  1  0 1 tan x   or tan x  1 4 Q2, Q4 Q1, Q3  1  tan   tan   1   4   45   14 2 x   ,180   x  180   ,360   x  45 ,180  45 x  180  14 2,360  14 2 x  45 , 225 x  16558,34558
  • 28.  ii  4sec2 x  3tan x  5 0  x  360 4  4 tan 2 x  3tan x  5 4 tan 2 x  3tan x  1  0  4 tan x  1 tan x  1  0 1 tan x   or tan x  1 4 Q2, Q4 Q1, Q3  1  tan   tan   1   4   45   14 2 x   ,180   x  180   ,360   x  45 ,180  45 x  180  14 2,360  14 2 x  45 , 225 x  16558,34558 x  45 ,16558, 225 ,34558
  • 29.  iii  cos 2  4cos 2   2sin 2  0    360
  • 30.  iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2 
  • 31.  iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2  3cos 2   sin 2 
  • 32.  iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2  3cos 2   sin 2  tan 2   3 tan    3
  • 33.  iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2  3cos 2   sin 2  Q1, Q2, Q3, Q4 tan 2   3 tan    3
  • 34.  iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan    3
  • 35.  iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60
  • 36.  iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300
  • 37.  iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300 (iv) cos 2  sin  , 0    360 2000 Extension 1 HSC Q2c)
  • 38.  iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300 (iv) cos 2  sin  , 0    360 2000 Extension 1 HSC Q2c) 1  2 sin 2   sin 
  • 39.  iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300 (iv) cos 2  sin  , 0    360 2000 Extension 1 HSC Q2c) 1  2 sin 2   sin  2 sin 2   sin   1  0
  • 40.  iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300 (iv) cos 2  sin  , 0    360 2000 Extension 1 HSC Q2c) 1  2 sin 2   sin  2 sin 2   sin   1  0 2 sin   1sin   1  0
  • 41.  iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300 (iv) cos 2  sin  , 0    360 2000 Extension 1 HSC Q2c) 1  2 sin 2   sin  2 sin 2   sin   1  0 2 sin   1sin   1  0 1 sin   or sin   1 2
  • 42.  iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300 (iv) cos 2  sin  , 0    360 2000 Extension 1 HSC Q2c) 1  2 sin 2   sin  2 sin 2   sin   1  0 2 sin   1sin   1  0 1 sin   or sin   1 2 Q1, Q2
  • 43.  iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300 (iv) cos 2  sin  , 0    360 2000 Extension 1 HSC Q2c) 1  2 sin 2   sin  2 sin 2   sin   1  0   2 sin   1sin   1  0 1 sin   or sin   1 2 Q1, Q2
  • 44.  iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300 (iv) cos 2  sin  , 0    360 2000 Extension 1 HSC Q2c) 1  2 sin 2   sin  2 sin 2   sin   1  0   2 sin   1sin   1  0 1 sin   or sin   1 2 Q1, Q2   270
  • 45.  iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300 (iv) cos 2  sin  , 0    360 2000 Extension 1 HSC Q2c) 1  2 sin 2   sin  2 sin 2   sin   1  0   2 sin   1sin   1  0 1 sin   or sin   1 1 2 sin   Q1, Q2   270 2   30
  • 46.  iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300 (iv) cos 2  sin  , 0    360 2000 Extension 1 HSC Q2c) 1  2 sin 2   sin  2 sin 2   sin   1  0    ,180     2 sin   1sin   1  0   30 ,180  30 1   30 ,150 sin   or sin   1 1 2 sin   Q1, Q2   270 2   30
  • 47.  iii  cos 2  4cos 2   2sin 2  0    360 cos 2   sin 2   4cos 2   2sin 2    3cos 2   sin 2  Q1, Q2, Q3, Q4   tan 2   3 tan   3 tan    3   60    ,180   ,180   ,360     60 ,180  60 ,180  60 ,360  60   60 ,120 , 240 ,300 (iv) cos 2  sin  , 0    360 2000 Extension 1 HSC Q2c) 1  2 sin 2   sin  2 sin 2   sin   1  0    ,180     2 sin   1sin   1  0   30 ,180  30 1   30 ,150 sin   or sin   1 1 2 sin   Q1, Q2   270 2   30   30 ,150 ,270
  • 48. (v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a)
  • 49. (v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos
  • 50. (v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos 2 sin 2   2 sin  cos  0
  • 51. (v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos 2 sin 2   2 sin  cos  0 2 sin  sin   cos   0
  • 52. (v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos 2 sin 2   2 sin  cos  0 2 sin  sin   cos   0 sin   0 or sin   cos 
  • 53. (v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos 2 sin 2   2 sin  cos  0 2 sin  sin   cos   0 sin   0 or sin   cos    0 ,180 ,360
  • 54. (v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos 2 sin 2   2 sin  cos  0 2 sin  sin   cos   0 sin   0 or sin   cos    0 ,180 ,360 tan   1
  • 55. (v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos 2 sin 2   2 sin  cos  0 2 sin  sin   cos   0 sin   0 or sin   cos    0 ,180 ,360 tan   1 Q1, Q3
  • 56. (v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos 2 sin 2   2 sin  cos  0 2 sin  sin   cos   0 sin   0 or sin   cos    0 ,180 ,360 tan   1 Q1, Q3  
  • 57. (v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos 2 sin 2   2 sin  cos  0 2 sin  sin   cos   0 sin   0 or sin   cos    0 ,180 ,360 tan   1 Q1, Q3 tan   1     45
  • 58. (v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos 2 sin 2   2 sin  cos  0 2 sin  sin   cos   0 sin   0 or sin   cos    0 ,180 ,360 tan   1 Q1, Q3 tan   1     45    ,180     45 ,180  45   45 , 225
  • 59. (v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos 2 sin 2   2 sin  cos  0 2 sin  sin   cos   0 sin   0 or sin   cos    0 ,180 ,360 tan   1 Q1, Q3 tan   1     45    ,180     45 ,180  45   45 , 225   0 ,45 ,180 ,225 ,360
  • 60. (v) 2sin 2   sin 2 , 0    360 1992 Extension 1 HSC Q2a) 2 sin 2   2 sin  cos 2 sin 2   2 sin  cos  0 2 sin  sin   cos   0 sin   0 or sin   cos    0 ,180 ,360 tan   1 Exercise 2D; Q1, Q3 2ac, 4ac, 5adgi, tan   1   9adgj, 10bdfij,   45 16, 24*    ,180     45 ,180  45   45 , 225   0 ,45 ,180 ,225 ,360