Trigonometric Equations Worksheet

Trigonometric Equations Worksheet

Read each question carefully and solve the trigonometric equations. Show all your work for full credit. Remember to find all solutions within the given interval or the general solution where specified.

1. Find all solutions for $2\sin(x) - 1 = 0$ in the interval $[0, 2\pi)$.

2. Determine the general solution for $\tan(x) = \sqrt{3}$.

3. If $\cos(2x) = 1/2$, the solutions for $x$ in $[0, 2\pi)$ are   and  .

4. The smallest positive solution for $\sin(3x) = -1$ is $x = $  .

5. Which of the following is a solution to $2\sin^2(x) + \cos(x) - 1 = 0$ in the interval $[0, 2\pi)$?

6. The equation $\sec^2(x) - \tan(x) - 1 = 0$ is equivalent to which of the following?

7. Find all solutions for $\sin(x)\cos(x) - \sin(x) = 0$ in the interval $[0, 2\pi)$.

8. Solve $2\cos^2(x) - 3\cos(x) + 1 = 0$ for $x \in [0, 2\pi)$.

9. The equation $\sin(x) = 2$ has no real solutions.

10. The general solution for $\cos(x) = 0$ is $x = \frac{\pi}{2} + 2n\pi$, where $n$ is an integer.