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