Pre-Calculus: Trigonometry functions

Five questions involving: Fundamental Identities, Trigonometric Functions, Trigonometric Equations, Sum and Difference Formulas, and Multiple Angle Formulas.

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Question 1: Using Fundamental Identities
Use the Pythagorean identity sin2 T + cos2 T = 1 to derive the other Pythagorean identities, 1 + tan2 T =
sec2 T and 1 + cot2 T = csc2 T. Discuss how to remember these identities and other fundamental
Question 2: Verify Trigonometric Functions
For each question:
A. Verify the identity.
B. Determine if the identity is true for the given value of x. Explain.
Question 3: Trigonometric Equations
1. Describe the difference between verifying a trigonometric identity and solving a trigonometric
2. Describe several techniques for solving trigonometric equations.
Question 4: Sum and Difference Formulas
1. You can write the sum and difference formulas for cosine as a single equation: cos (u ± v) = cos u cos
v ± sin u sin v. Explain why the symbol ± is used on the left side, but the symbol ± is used on the right
side. Then use the symbols ± and ± to write the sum and difference formulas for sine and tangent as
single equations.
Question 5: Multiple Angle Formulas
1. Describe how you can use a double-angle formula or a half-angle formula to derive the formula for the
area of an isosceles triangle. Use a labeled sketch to illustrate your derivation. Then write two
examples that show how your formula can be used.

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