Without using a calculator, express the principal value of $\cos^{-1} \frac{\sqrt{2}}{2}$ in degre

Question

Without using a calculator, express the principal value of $\cos^{-1} \frac{\sqrt{2}}{2}$ in degrees, $\sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)$ in radians in terms of $\pi$, $\tan^{-1}(-\sqrt{3})$ in degrees, $\cos^{-1} 1$ in radians in terms of $\pi$, $\sin^{-1} \frac{1}{2}$ in degrees, and $\tan^{-1}(-1)$ in radians in terms of $\pi$.

Accepted Answer

(i) $45^\circ$; (ii) $-\dfrac{\pi}{3}$; (iii) $-60^\circ$; (iv) $0$; (v) $30^\circ$; (vi) $-\dfrac{\pi}{4}$

Trigonometry - Inverse Trigonometric Functions

Trigonometry - Inverse Trigonometric Functions

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