Solving Sine and Cosine Equations
This worksheet focuses on solving sine and cosine trigonometric equations for Grade 10 students, covering various levels of complexity.
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Standards
Topics
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
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