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Trigonometric Identities

Published on 01/17/2011

Activity Overview

Students will verify, prove, and explore trigonometric identities symbolically, numerically, and graphically.

Key Steps

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    Students will use the VERITRIG program to help prove the two trigonometric identities. They will use the Text tool to label a triangle drawn within the unit circle. Then students will write x and y in terms of cosθ and sinθ to prove the identity cos2θ + sin2θ = 1.

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    Students then prove the identity sec2θ = 1 + tan2θ using similar triangles and ratios.

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    After proving the identities, students can use the cosine and sine values of the angles in the unit circle to prove that the proof holds for each identity.