Worksheet Chapter 6: Ratios and Graphs of Trigonometric Functions

1. True or False: The tangent function y = tan x has an amplitude of 1.

2. Solve the equation sin x = 0.5 for 0° ≤ x ≤ 360°.

3. State the reference angle for θ = 300°.

4. Find the exact value of cos(240°) - sin(330°).

5. Fill in the blank: The acute angle formed between the terminal side of an angle θ and the x-axis is called the ________ angle.

6. Given cos θ = -513 and 90° ≤ θ ≤ 180°, calculate the exact value of (a) sin θ, and (b) tan θ.

7. A trigonometric function is given by y = 3 cos(2x) + 2 for 0° ≤ x ≤ 360°. (a) State the maximum and minimum values of y. (b) Find the period of the function. (c) Determine the values of x at which y reaches its maximum value.

8. Which quadrant contains an angle θ where sin θ < 0 and cos θ < 0?

9. True or False: cos(180° - θ) = -cos θ for any acute angle θ.

10. For the curve y = 4 sin(3x), state (a) its amplitude and (b) its period.