to understand statics & daynamics

1. 00 30 /6 45/4 60 /3 90 /2
sin 0 1/2 2 /2 3/2 1
cos 1 3/2 2 /2 1/2 0
tan 0 3/3 1 3 --
cot -- 3 1 3/3 0
sec 1 2 3/3 2 2 --
csc -- 2 2 2 3/3 1
Fundamental Trigonometry Concepts Needed for Calculus
sin A =
hyp
opp
r
y
c
a

cos A =
hyp
adj
r
x
c
b

tan A =
adj
opp
x
y
b
a
 cot A =
opp
adj
y
x
a
b
 sec A =
adj
hyp
x
r
b
c
 csc A =
opp
hyp
y
r
a
c

1. Reciprocal Functions: csc A =
Asin
1
; cot A =
Atan
1
; sec A =
Acos
1
2. Cofuntions: sin & cos, tan & cot, sec & csc. Any function of an angle less than 90 is equal to the
cofunction of its complement (i.e. 90 - A).
3. Signs on the trig functions I the four quadrants are:
All trig functions are positive in Q I. cos and sec are negative in Q II and Q III
sin & csc are negative in Q III & Q IV tan and cot are negative in Q II and Q IV
4. To take the function of an angle A greater than 90 and reduce it to the same function of an angle less
than 90 first determine the sign on that function in that particular quadrant and then:
i) if A is in Q II, use 180 - A; ii) if A is in Q III, use A - 180; iii) if A is in Q IV use 360 - A.
5. FUNDAMENTAL RELATIONSHIPS:
sin (-) = - sin ; cos (-) = cos ; sin2
 + cos2
 = 1 for all .
 sincoscossin)sin(   sinsincoscos)cos( 
6. Other relationships that follow from (5) above are: tan2
 + 1 = sec2
 & 1 + cot2
 = csc2

cos 2 = cos2
 - sin2
; sin 2 = 2 sin  cos ;
2
2cos1
cos2 


 ;
2
2cos1
sin2 



7.Relationship between degrees and radians (a pure number, no units): o
DR
180


; R-radians; D-degrees
8. Basic trig values: or
sin 0 = 0 /2 = 0.000 = cos 90
sin /6 = 1 /2 = 0.500 = cos 60
sin /4 = 2 /2 = 0.707 = cos 45
sin /3 = 3 /2 = 0.866 = cos 30
sin /2 = 4 /2 = 1.000 = cos 0