Grade 12 Trigonometry: Sine and Cosine Equations
This worksheet focuses on solving sine and cosine equations, including those with multiple solutions and transformations, suitable for Grade 12 trigonometry students.
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Grade 12 Trigonometry: Sine and Cosine Equations
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Read each question carefully and solve the trigonometric equations. Show all your work for full credit. Unless otherwise specified, find all solutions in the interval [0, 2π).
1. Solve for x: 2sin(x) - 1 = 0
2. Find all solutions for x: √3cos(x) + 2 = 1
3. The general solution for sin(2x) = 1/2 is x = or x = , where n is an integer.
4. If cos(3x) = -1, the smallest positive solution for x is .
5. Which of the following is a solution to the equation sin(x)cos(x) = 1/4?
π/12
π/8
π/6
π/4
6. The equation cos(x) = 2 has no real solutions.
True
False
7. Solve for x in the interval [0, 2π): 2cos²(x) + sin(x) - 1 = 0
8. Find all solutions for x: sin(x) = cos(x)