IB Mathematics Analysis and Approaches 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 $\tan (x)=-\sqrt{3}$.