Question Type 1: Determining relationship between trigonometric functions using unit circle Exercises

Solve $\sin\left(x+\frac{\pi}{4}\right)=\cos\left(\frac{\pi}{4}\right)$ for $x\in[0,2\pi)$.

Find all $x$ in $(-2\pi,2\pi)$ for which $\cot(x)=0$.

Determine all $x$ in $[0, 2\pi)$ such that $\sin(x)=\sin(5\pi/6)$.

Solve $\sin(2x)=\sin(\pi/3)$ for $x\in(-2\pi,2\pi)$.

Find the principal value of $\arccos(-\sqrt{3}/2)$ and list all solutions to $\cos(x)=-\sqrt{3}/2$ in $(-2\pi,2\pi)$.

Solve $\csc(x)=2$ for $x$ in $(-2\pi, 2\pi)$.

Find all $x \in (-2\pi, 2\pi)$ such that $\cos(x) = -\frac{1}{2}$.

Solve $\sec(x)=\sqrt{2}$ for $x\in(-2\pi,2\pi)$.

Find all $x$ in $(-\pi,\pi]$ satisfying $\tan(x)=\tan(-\pi/4)$.

Find all values of $x$ in $(-2\pi, 2\pi)$ such that $\cos(x)=\cos\left(\frac{\pi}{6}\right)$.

Find all $x$ in $(-2\pi, 2\pi)$ such that $\sin(x) = \cos\left(\frac{\pi}{3}\right)$.

Determine all $x$ in $(-2\pi, 2\pi)$ satisfying $\tan(x) = -\sqrt{3}$.