Question Type 3: Solving inverse trigonometric functions using the triangle method Exercises

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

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

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

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

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

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