Do You Know Inverse Trigonometric Graphs?

Geometry Level 2

$\displaystyle{\sin^{-1} (\color{#3D99F6} {\alpha})-\cos^{-1}(1) = \dfrac{\pi}{3}}$

Find the value of $\color{#3D99F6} {\alpha}$ to 3 decimal places.

Clarification : Angles are measured in radians.

1 solution

Samara Simha Reddy
Mar 10, 2016

$\displaystyle{\sin^{-1} (\alpha)-\cos^{-1}(1) = \frac{\pi}{3}}$

$\displaystyle{\sin^{-1} (\alpha) - 0 = \frac{\pi}{3}}$

Since $\cos^{-1}(1)$ = 0

$\alpha$ = $\displaystyle{\sin (\frac{\pi}{3}}$ )

$\alpha$ = $\dfrac{\sqrt3}{2}$

$\alpha$ $\approx$ $\boxed{0.866}$ .

Because $\theta$ is often used to denote an angle instead of a real number, I've edited the problem to use $\alpha$ instead.

Calvin Lin Staff - 5 years, 3 months ago

Thanks for editing of my problem Sir.

A Former Brilliant Member - 5 years, 2 months ago