The document contains mathematical equations and identities relating trigonometric functions for various angle transformations including opposite, complementary, and coterminal angles. It shows relationships between sin, cos, tan, cot, sec, and csc functions when the angle is replaced with its opposite, complementary, or coterminal value.

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7. M(DOM) =  M(DON) = - 
(NOH (a
ODM ONH (b
OD = OH MD = NH (c
M cos  sin  ) N ( cos ( -  ) sin ( -  ) (d
cos ( -  ) = sin  sin ( -  ) = cos 
2

2

2

2

2
Y
X
N
M
H
-1 DO 1
1
-1
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

8. Cos ( -  ) = sin  tan ( -  ) = cot  sec ( -  ) = csc 
Sin ( -  ) = cos  cot ( -  ) = tan  csc ( -  ) = sec 
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2

2

2

2

2

2

9. sin ( - ) = - cos 
2
Sin ( - ) = sin  - ( -  )  b – a = - ( a – b )
= - sin ( -  ) sin (- ) = - sin ( )
= - cos  sin ( -  ) = cos 
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2

2

2

2

10. cos( - ) = sin
2
cos ( - ) = cos  - ( -  )  b – a = - ( a – b )
= cos ( -  ) cos (- ) = cos ( )
= sin  cos( -  ) = sin 
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2

2

2

2

11. Csc ( - ) = - sec 
2
Sin 
1
csc ( - ) = csc  - ( -  )  b – a = - ( a – b )
= csc  =
= sin ( -  ) = - sin 
= = - sec  sin ( -  ) = cos 

2

2
Sin - ( -  )
2
- Sin ( -  )
2
Cos
-1

2

12. sec ( - ) = csc 
2
sec( - ) = sec  - ( -  )  b – a = - ( a – b )
= sec =
= cos( -  ) = cos 
= = csc  cos ( -  ) = sin 

2

2
Cos - ( -  ) 
2
cos 
1
cos ( -  )
2
Sin 
1

2