PreCalculus
Activity:
Trigonometric Proofs
Posted on Apr 17, 2008
Topic: Trigonometric Identities
Students will perform trigonometric proofs and use the graphing capabilities of the handheld for verification.
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Activity Key Steps:
In this activity, students use their handhelds to verify trigonometric proofs. In problem 1, students prove (sin(x))(csc(x)) = 1 and verify their answer.
They will see if the graph of the expression on the left side of the equation coincides with the graph of the expression on the right side of the equation.
Problem 2 asks students to prove (1 + cos(x))(1-cos(x)) = sin^2(x).
They graph the expressions.
In problem 3. students prove and graph (sin(x))(cot(x))(sec(x)) = 1.
In problem 4, students are given sec^2(x-1)/sec^2(x) = sin^2(x). They prove the expression by using trigonometric identities.
Problem 5 and 6 are more complex. Students prove that the expressions are true and then graph them to verify.
At the end of this activity, students will be able to use fundamental trigonometric identities to prove more complex trigonometric identities. They will be able to verify these identities by graphing.