Question Type 5: Solving simple expressions for the value of x Exercises

Solve $\cos(2x)=-\frac{1}{2}$ for $0^{\circ}\le x<360^{\circ}$.

Solve for $x$ in $[0^\circ,180^\circ)$: $\tan x = 1$

Solve $\sin x+\sin(2x)=0$ for $0\le x<2\pi$.

Solve $\sec x=2$ for $0 \leqslant x < 2\pi$.

Solve for $x$ in $[0^\circ, 360^\circ)$: $2\cos^2 x - 1 = 0$

Solve $\sin(3x)=\frac{\sqrt{3}}{2}$ for $0\le x<2\pi$.

Solve the equation $\cos 2x = \frac{1}{2}$ for $0^\circ \le x < 360^\circ$.

Solve $3\cos(3x)=1$ for $0\le x<2\pi$.

Solve for $x$ in $[0^\circ, 360^\circ)$: $\sin 3x = \frac{\sqrt{3}}{2}$

Solve $\tan\left(x-\frac{\pi}{6}\right)=1$ for the general solution.

Solve for $x$ in $[0^\circ,360^\circ)$: $\sin\bigl(\tfrac{x}{2}\bigr) = \tfrac12$

Solve $2\sin(2x)=1$ for $0\le x<2\pi$.