IB Mathematics Analysis and Approaches Question Type 3: Solving Inverse Trigonometric Functions Using the Triangle Method Exercises

Find $\tan (\arcsin (\frac{2}{x}))$ expressed in terms of $x$, where $x>2$.

Simplify $\cot (\arcsin (x/7))$ in terms of $x$.

Evaluate $\tan (\arccos (5/13))$.

Simplify $\cos (\arctan (2x/3))$ in terms of $x$.

Solve for $x$: $\sin (\arctan (x/3))=3/5$.

Prove that $\sin (\arccos (x))=\sqrt{1-x^2}$ for $-1\le x\le 1$.

Simplify $\sec \left(\arctan \left(\frac{x}{4}\right)\right)$ in terms of $x$.

Find $\sin \left(\arccos \left(\frac{x-1}{5}\right)\right)$ in terms of $x$.

Express $\sin (\arctan (3x))$ in terms of $x$.

Express $\cos (\arcsin (x/3))$ in terms of $x$.

Simplify $\sin (\arccos (x/5))$ in terms of $x$.

Evaluate $\cos \left(\arcsin \left(\frac{4}{5}\right)\right)$.