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 .
slide4

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

  • we must first find the
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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