Solving Sine and Cosine Equations

This worksheet focuses on solving sine and cosine trigonometric equations for Grade 10 students, covering various levels of complexity.

Grade 10 Math TrigonometrySine and Cosine Equations

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Includes

2 Short AnswerFill in the BlanksMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.HSF.TF.A.3CCSS.MATH.CONTENT.HSF.TF.C.8

Topics

TrigonometrySineCosineEquationsGrade 10

7 sections · Free to use · Printable

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Solving 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. Unless otherwise specified, find all solutions in the interval [0, 2π).

1. Solve for x: sin(x) = 1/2

2. Solve for x: cos(x) = -√3/2

3. The general solution for sin(x) = 0 is x = , where n is an integer.

4. If cos(x) = 1, then the principal value of x is .

5. Which of the following is a solution to 2sin(x) + 1 = 0?

π/6

7π/6

π/3

2π/3

6. Find all solutions for 4cos²(x) - 3 = 0 in the interval [0, 2π).

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

8. The equation sin(x) = 2 has no real solutions.

True

False

9. The general solution for cos(x) = -1 is x = π + 2nπ, where n is an integer.

True

False