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Pre-Calculus/Trig3
5.1 Trigonometric Identities
Name
Block
Date
There are three main types of trigonometric identities.
,
,
Type I: Reciprocal Identities
Sin  =
Csc  =
Cos  =
Sec  =
Tan  =
Cot  =
Type II: Quotient Identities
Given
Rewrite with
opp, adj, and hyp
sin 
cos 
Tan  =
Simplify fraction
Cot  =
Type III: Pythagorean Identities
Pythagorean Theorem:
Rewrite using x,y,r:
Rewrite using trig:
**1st identity
Divide by sin2  :
**2nd identity
Divide 1st identity by cos2  :
**3rd identity
Rewrite as
one trig function
Pre-Calculus/Trig3
5.1 Basic Trigonometric Identities
Worksheet
Solve for the values
in the 1st quadrant.
2
1. If sin  = , find cos  .
3
Name
Block
Date
Express each as a function
of a 1st quadrant angle.
Simplify to one trig function.
2. cos 892o =
3.
sin 2  cot 
=
cos 
Practice Problems:
Solve for the values in the 1st quadrant.
4. If tan  = 2, find cot  .
7. If sin  =
7
, find cot  .
10
5. If cos  =
1
, find tan  .
4
7
8. If tan  = , find sin  .
2
Express each function as a function of a 1st quadrant angle.
10. sin 458o =
11. tan (-876o) =
Simplify to one trig function.
cot 
13.
=
tan 
14. sin2  cos2  -cos2 
6. If tan  =3, find sec  .
9. If sec  =
4
, find sin  .
3
12. csc 495o =
15. cos  +sin  tan 