Double angle and half angle identities
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Double-Angle and Half Angle Identities. Double-Angle Identity. If represents the measure of an angle, then the following identities hold for all values of . If and terminates in the first quadrant, find the exact value of each function. -1.

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Double angle identity
Double-Angle Identity

  • If represents the measure of an angle, then the following identities hold for all values of .


  • If and terminates in the first quadrant, find the exact value of each function.

-1


  • If and terminates in the first quadrant, find the exact value of each function.

  • we must first find the



If and terminates in the first quadrant find the exact value of each function
If and terminates in the first quadrant, find the exact value of each function.


Half angle identities
Half-Angle Identities

  • If represents the measure of an angle, then the following identities hold for all values of .


Use a half angle identity to find the exact value of each function
Use a half-angle identity to find the exact value of each function.

Since 15⁰ is a first quadrant angle and sine is positive in the first quadrant, choose the positive value.


Use a half angle identity to find the exact value of each function1
Use a half-angle identity to find the exact value of each function.

Since 135 is a second quadrant angle and cosine is negative in the second quadrant, choose the negative value. Thus,




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