Algebra II
Activity:
Proof of Identity
Posted on Apr 24, 2008
Topic: Trigonometric Identities
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.
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Activity Key Steps:
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.
In problem 2, students explore negative angle indentities.
Students can reshape the curve but not reposition it to show that sin(–x) = –sin(x).
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.
Students will move on to problem 4 and explore Pythagorean identities.
At the end of this activity, students will be familiar with the types of trigonometric identities. They will be able to verify them by graphing and use Pythagorean Theorem to prove sin^2 + cos^2(radian) = 1 and sec^2(radian) = 1 + tan^2(radian).