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Trigonometric Equations Using Half Angle Formulas

Simplifying all six trigonometric functions with half a given angle.

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Angle Identities

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Double Angle Identity

 double angle identity relates the a trigonometric function of two times an argument to a set of trigonometric functions, each containing the original argument.

cos(α+α)=cosαcosαsinαsinαcos2α=cos2αsin2α

There are ways in which you can manipulate the double angle identity which causes there to be three ways you can present the double angle identity.

cos2α=cos2αsin2αcos2α=2cos2α1cos2α=12sin2α

Hint: This double angle identity comes in handy when you are trying to solve proofs

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Half Angle Identity

 half angle identity relates the a trigonometric function of one half of an argument to a set of trigonometric functions, each containing the original argument.

sinα2=1cosα2 if α2 is located in either the first or second quadrant.

sinα2=1cosα2 if α2 is located in the third or fourth quadrant.

cosα2=1+cosα2 if α2 is located in either the first or fourth quadrant.

cosα2=1+cosα2 if α2 is located in either the second or fourth quadrant.

Tip: This all depends how the values of cosine and sine are negative dependig which quadrant cosine or sine lies on.

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