Education Technology

Proof of Identity

Activity Overview

Students use graphs to verify the reciprocal identities. They then use the handheld's manual graph manipulation feature to discover the negative angle, cofunction, and Pythagorean trigonometric identities. Geometric proofs of these identities are given as well.

Key Steps

  • Image

    In problem 1, students will investigate the idea that two functions are equal if their graphs are exactly the same.
    Students will also investigate the reciprocal of an identity. Students should se that a reciprocal identity shows that one trigonometric function is equal to the reciprocal of another.

  • Image

    In problem 2, students explore negative angle indentities.

    Students can reshape the curve but not reposition it to show that sin(–x) = –sin(x).

  • Image

    Problem 3, gives students an opportunity to explore cofunction identities. Students will see that sine and cosine functions are similar to each other, as compared to the tangent function.

    Students graph sin(x) and cos(–x). They will learn that the idea of sine and cosine being similar can be formalized by the cofunction identities.