5.7 Practice (#1-4, 5-25 odds)

1. 1. Solve the equation on the interval (0 ≤ θ ≤ 2π): 1 - cos θ = 1/2.

• θ = π/3, 5π/3

• θ = π/2, 3π/2

• θ = π/4, 7π/4

• θ = 0, 2π

2. 2. Solve the equation on the interval (0 ≤ θ ≤ 2π): 4 cos^2 θ = 1.

• θ = π/3, 2π/3, 4π/3, 5π/3

• θ = π/4, 3π/4, 5π/4, 7π/4

• θ = π/6, 5π/6, 7π/6, 11π/6

• θ = 0, π, 2π

3. Solve the equation on the interval (0 ≤ θ ≤ 2π): 4 sin^2 θ - 3 = 0.

• θ = π/6, 5π/6, 7π/6, 11π/6

• θ = π/3, 2π/3, 4π/3, 5π/3

• θ = π/4, 3π/4, 5π/4, 7π/4

• θ = 0, π/2, π, 3π/2

4. Solve the equation on the interval (0 ≤ θ ≤ 2π): √3 cot θ + 1 = 0. Select the correct θ value:

• π/3

• π/6

• 2π/3

• 5π/3

• 3π/2

5. 5. Solve the equation on the interval (0 ≤ θ ≤ 2π): cos(2θ) = -1/2.

• θ = π/6, 11π/6

• θ = π/3, 5π/3

• θ = 2π/3, 4π/3

• θ = 5π/6, 7π/6

7. Solve the equation: cos(2θ - π/2) = -1.

• 3π/4

• π/4

• 5π/4

• 7π/4

• 0

7. 9. Solve the equation on the interval (0 ≤ θ ≤ 2π).

Give a general formula for all the solutions.

Solve the equation: sin(2θ) = -1/2.

• θ = 7π/12

• θ = 7π/6

• θ = 11π/12

• θ = 11π/6

7. 11. Solve the equation on the interval (0 ≤ θ ≤ 2π).

Give a general formula for all the solutions.

Solve the equation: tan(θ/2) = -1.

• θ = 3π/2

• θ = π

• θ = 2π

• θ = 2π/3

• θ = 3π/4

Use a graphing utility to solve the equation. Round answers to two decimal places:

( x + 5 cos x = 0 ). What is the approximate value of x?

• -1.31

• 1.98

• 3.84

• No real solution

• 0

Answer explanation

15. Use a graphing utility to solve the equation. Round answers to two decimal places:

( sin x - cos x = x ). Which of the following is closest to a solution?

• -1.26

• 0.0

• 1.56

• 1.3

• no solution

Answer explanation