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

identities.

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

equation.

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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