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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