Sine and Cosine Equations Worksheet

Solve sine and cosine equations, understand periodic functions, and identify general solutions for trigonometric equations.

Grade 9 Math TrigonometrySine and Cosine Equations

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Includes

2 Short AnswerFill in the BlanksMultiple ChoiceCustomTrue / False

Standards

CCSS.MATH.CONTENT.HSF.TF.A.3CCSS.MATH.CONTENT.HSF.TF.B.7

Topics

TrigonometrySineCosineEquationsGrade 9

8 sections · Free to use · Printable

Sine and Cosine Equations

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Read each question carefully and solve for the unknown variable. Show all your work for full credit.

1. Solve the equation 2sin(x) - 1 = 0 for x in the interval [0, 2π).

2. Find all solutions for cos(x) + 1 = 0.

3. The general solution for sin(x) = 1/2 is x = π/6 + 2nπ and x = + 2nπ, where n is an integer.

4. If cos(x) = -√3/2, then one set of solutions is x = 5π/6 + 2nπ. The other set of solutions is x = + 2nπ.

5. Which of the following is a solution to the equation sin(x) = -1?

π/2

3π/2

6. For what values of x in [0, 2π) is cos(x) = 0?

0, π

π/2, 3π/2

π/2, 2π

0, 2π

7. Solve 2cos²(x) - 1 = 0 for x in the interval [0, 2π).

8. Find the general solution for sin(2x) = √3/2.

Refer to the unit circle diagram below for questions involving radian measures.

9. The sine function has a period of 2π.

True

False

10. The equation cos(x) = 2 has no real solutions.

True

False