∫Calc Practice
Home›Calculus 1›Solving trigonometric equations

Solving trigonometric equations practice problems

Solve trigonometric equations on 0 ≤ θ < 2π, including ones that factor. 60 problems with worked solutions; in 60 of them every equation is proved by a computer algebra system.

Solve \( \displaystyle 2 \sin{\left(\theta \right)} = -1 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.76easy✓ Every equation proved
Solve \( \displaystyle 2 \cos{\left(\theta \right)} = \sqrt{3} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.81easy✓ Every equation proved
Solve \( \displaystyle 2 \sin{\left(\theta \right)} = 1 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.84easy✓ Every equation proved
Solve \( \displaystyle \cos{\left(\theta \right)} = - \frac{1}{2} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.85easy✓ Every equation proved
Solve \( \displaystyle \tan{\left(\theta \right)} = \frac{\sqrt{3}}{3} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.86easy✓ Every equation proved
Solve \( \displaystyle \cos{\left(\theta \right)} = - \frac{\sqrt{3}}{2} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.87easy✓ Every equation proved
Solve \( \displaystyle \cos{\left(\theta \right)} = 0 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.89easy✓ Every equation proved
Solve \( \displaystyle 2 \sin{\left(\theta \right)} = - \sqrt{2} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.90easy✓ Every equation proved
Solve \( \displaystyle \tan{\left(\theta \right)} = - \sqrt{3} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.252easy✓ Every equation proved
Solve \( \displaystyle \sin{\left(\theta \right)} = \frac{1}{2} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.256easy✓ Every equation proved
Solve \( \displaystyle 2 \cos{\left(\theta \right)} = - \sqrt{2} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.257easy✓ Every equation proved
Solve \( \displaystyle 2 \tan{\left(\theta \right)} = \frac{2 \sqrt{3}}{3} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.263easy✓ Every equation proved
Solve \( \displaystyle \tan{\left(\theta \right)} = \sqrt{3} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.264easy✓ Every equation proved
Solve \( \displaystyle 2 \tan{\left(\theta \right)} = 2 \sqrt{3} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.324easy✓ Every equation proved
Solve \( \displaystyle \sin{\left(\theta \right)} = 0 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.325easy✓ Every equation proved
Solve \( \displaystyle \sin{\left(\theta \right)} = \frac{\sqrt{3}}{2} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.327easy✓ Every equation proved
Solve \( \displaystyle \cos{\left(\theta \right)} = -1 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.329easy✓ Every equation proved
Solve \( \displaystyle 2 \sin{\left(\theta \right)} = \sqrt{3} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.331easy✓ Every equation proved
Solve \( \displaystyle \cos{\left(\theta \right)} = \frac{\sqrt{2}}{2} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.401easy✓ Every equation proved
Solve \( \displaystyle \tan{\left(\theta \right)} = 1 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.403easy✓ Every equation proved
Solve \( \displaystyle \sin{\left(\theta \right)} = \frac{\sqrt{2}}{2} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.404easy✓ Every equation proved
Solve \( \displaystyle 2 \tan{\left(\theta \right)} = - 2 \sqrt{3} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.405easy✓ Every equation proved
Solve \( \displaystyle 2 \tan{\left(\theta \right)} = - \frac{2 \sqrt{3}}{3} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.406easy✓ Every equation proved
Solve \( \displaystyle \cos{\left(\theta \right)} = 1 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.407easy✓ Every equation proved
Solve \( \displaystyle 2 \cos{\left(\theta \right)} = 1 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.408easy✓ Every equation proved
Solve \( \displaystyle 2 \cos{\left(\theta \right)} = \sqrt{2} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.409easy✓ Every equation proved
Solve \( \displaystyle \sin{\left(\theta \right)} = - \frac{\sqrt{2}}{2} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.410easy✓ Every equation proved
Solve \( \displaystyle 2 \sin{\left(\theta \right)} = - \sqrt{3} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.482easy✓ Every equation proved
Solve \( \displaystyle \tan{\left(\theta \right)} = -1 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.484easy✓ Every equation proved
Solve \( \displaystyle \cos{\left(\theta \right)} = \frac{\sqrt{3}}{2} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.485easy✓ Every equation proved
Solve \( \displaystyle 2 \sin{\left(\theta \right)} = \sqrt{2} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.487easy✓ Every equation proved
Solve \( \displaystyle 2 \cos{\left(\theta \right)} = - \sqrt{3} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.488easy✓ Every equation proved
Solve \( \displaystyle 2 \cos^{2}{\left(\theta \right)} + \cos{\left(\theta \right)} = 0 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.77medium✓ Every equation proved
Solve \( \displaystyle 2 \sin^{2}{\left(\theta \right)} + \sin{\left(\theta \right)} - 1 = 0 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.78medium✓ Every equation proved
Solve \( \displaystyle \sin{\left(2 \theta \right)} = \frac{\sqrt{2}}{2} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.79medium✓ Every equation proved
Solve \( \displaystyle \sin{\left(2 \theta \right)} = 1 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.80medium✓ Every equation proved
Solve \( \displaystyle \sin{\left(2 \theta \right)} = 0 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.82medium✓ Every equation proved
Solve \( \displaystyle 2 \cos^{2}{\left(\theta \right)} - \cos{\left(\theta \right)} = 0 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.83medium✓ Every equation proved
Solve \( \displaystyle 2 \sin^{2}{\left(\theta \right)} - 2 \sin{\left(\theta \right)} = 0 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.88medium✓ Every equation proved
Solve \( \displaystyle \sin{\left(2 \theta \right)} = \frac{\sqrt{3}}{2} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.251medium✓ Every equation proved
Solve \( \displaystyle \sin{\left(2 \theta \right)} = -1 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.253medium✓ Every equation proved
Solve \( \displaystyle \sin{\left(2 \theta \right)} = - \frac{\sqrt{3}}{2} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.254medium✓ Every equation proved
Solve \( \displaystyle 2 \cos^{2}{\left(\theta \right)} + 2 \cos{\left(\theta \right)} = 0 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.255medium✓ Every equation proved
Solve \( \displaystyle 2 \cos^{2}{\left(\theta \right)} - 3 \cos{\left(\theta \right)} + 1 = 0 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.258medium✓ Every equation proved
Solve \( \displaystyle 2 \cos^{2}{\left(\theta \right)} - 2 \cos{\left(\theta \right)} = 0 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.259medium✓ Every equation proved
Solve \( \displaystyle \sin{\left(2 \theta \right)} = - \frac{1}{2} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.260medium✓ Every equation proved
Solve \( \displaystyle 2 \cos^{2}{\left(\theta \right)} + \cos{\left(\theta \right)} - 1 = 0 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.261medium✓ Every equation proved
Solve \( \displaystyle 2 \sin^{2}{\left(\theta \right)} - 2 = 0 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.262medium✓ Every equation proved
Solve \( \displaystyle 2 \sin^{2}{\left(\theta \right)} - 3 \sin{\left(\theta \right)} + 1 = 0 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.265medium✓ Every equation proved
Solve \( \displaystyle 2 \cos^{2}{\left(\theta \right)} - \cos{\left(\theta \right)} - 1 = 0 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.322medium✓ Every equation proved
Solve \( \displaystyle 2 \sin^{2}{\left(\theta \right)} + \sin{\left(\theta \right)} = 0 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.323medium✓ Every equation proved
Solve \( \displaystyle 2 \sin^{2}{\left(\theta \right)} - \sin{\left(\theta \right)} = 0 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.326medium✓ Every equation proved
Solve \( \displaystyle \sin{\left(2 \theta \right)} = - \frac{\sqrt{2}}{2} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.328medium✓ Every equation proved
Solve \( \displaystyle 2 \sin^{2}{\left(\theta \right)} - \sin{\left(\theta \right)} - 1 = 0 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.330medium✓ Every equation proved
Solve \( \displaystyle 2 \cos^{2}{\left(\theta \right)} - 2 = 0 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.402medium✓ Every equation proved
Solve \( \displaystyle 2 \sin^{2}{\left(\theta \right)} + 3 \sin{\left(\theta \right)} + 1 = 0 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.479medium✓ Every equation proved
Solve \( \displaystyle 2 \sin^{2}{\left(\theta \right)} + 2 \sin{\left(\theta \right)} = 0 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.480medium✓ Every equation proved
Solve \( \displaystyle 2 \cos^{2}{\left(\theta \right)} + 3 \cos{\left(\theta \right)} + 1 = 0 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.481medium✓ Every equation proved
Solve \( \displaystyle 2 \cos^{2}{\left(\theta \right)} - \frac{1}{2} = 0 \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.483medium✓ Every equation proved
Solve \( \displaystyle \sin{\left(2 \theta \right)} = \frac{1}{2} \) for \( \displaystyle 0 \le \theta < 2\pi \).
Problem 13.486medium✓ Every equation proved