Geometry

# Inverse Trigonometric Functions

If $\sin^{-1}\left(\frac{1}{2}\right) = \theta^\circ$, where $-90 \leq \theta \leq 90$, what is the value of $\theta$?

What is the value of $\cos^{-1} \left(- \frac { \sqrt{3} } {2} \right)$ (in degrees)?

Which of the following is equal to $\tan^{-1} \left( 1 \right) ?$

$ABC$ is a right triangle with hypotenuse $35$, and has an angle $\alpha$ that is equal to $\sin^{-1}\left(\frac{3}{5}\right)$. $XYZ$ is a right triangle with hypotenuse $143$, and has an angle $\beta$ that is equal to $\cos^{-1}\left(\frac{5}{13}\right)$. What is the sum of the perimeter of both right triangles?

The domain of the inverse trigonometric function $\sin^{-1}$ is $[ -a, b ].$ What is the value of $a + b?$

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