Double angle and half angle identities
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Double-Angle and Half Angle Identities PowerPoint PPT Presentation


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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 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


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

  • we must first find the


  • we must find to use the identity for .


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


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.

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 function.

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


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


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