Linear Trigonometric Equations - Video Tutorials & Practice Problems

Find all solutions to the equation.

$\cos x=1$

• A. $x=0$
• B. $x=2\pi n$
• C. $x=\pi+2\pi n$
• D. $x=\frac{\pi}{2}+2\pi n,x=\frac{3\pi}{2}+2\pi n$

Find all solutions to the equation.

$\tan\theta=1$

• A. $\theta=2\pi n$
• B. _$\theta=\frac{\pi}{4}+2\pi n$
• C. $\theta=\frac{\pi}{4}+\pi n$
• D. $\theta=\frac{5\pi}{4}+2\pi n$

Find all solutions to the equation.

$\sin\theta=-\frac{\sqrt3}{2}$

• A. $\theta=\frac{\pi}{3}+2\pi n,\frac{2\pi}{3}+2\pi n$
• B. $\theta=\frac{7\pi}{6}+2\pi n,\frac{11\pi}{6}+2\pi n$
• C. $\theta=\frac{4\pi}{3}+2\pi n,\frac{5\pi}{3}+2\pi n$
• D. $\theta=\frac{\pi}{6}+2\pi n,\frac{5\pi}{6}+2\pi n$

Find all solutions to the equation.

$3\sin\theta-6=-9$

• A. $\theta=\frac{\pi}{2}+2\pi n$
• B. $\theta=2\pi n$
• C. $\theta=\pi+2\pi n$
• D. $\theta=\frac{3\pi}{2}+2\pi n$

Find all solutions to the equation.

$\sqrt2\cos\theta+4=5$

• A. $\theta=\frac{\pi}{4}+2\pi n,\frac{3\pi}{4}+2\pi n$
• B. $\theta=\frac{\pi}{4}+2\pi n,\frac{7\pi}{4}+2\pi n$
• C. $\theta=\frac{3\pi}{4}+2\pi n,\frac{5\pi}{4}+2\pi n$
• D. $\theta=\frac{5\pi}{4}+2\pi n,\frac{7\pi}{4}+2\pi n$

Find all solutions to the equation.

$\sqrt3\tan\theta-7=-6$

• A. $\theta=\frac{\pi}{6}+2\pi n,\frac{5\pi}{6}+2\pi n$
• B. $\theta=\frac{5\pi}{6}+2\pi n,\frac{11\pi}{6}+2\pi n$
• C. $\theta=\frac{\pi}{6}+2\pi n,\frac{7\pi}{6}+2\pi n$
• D. $\theta=\frac{\pi}{6}+\pi n$