Sine and Cosine Equations Worksheet
Solve sine and cosine equations, understand periodic functions, and identify general solutions for trigonometric equations.
Includes
Standards
Topics
Sine and Cosine Equations
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Date:
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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?
0
π/2
π
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
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