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Trigonometric Functions

SOH-CAH-TOA! Have you heard the call of the trig function? Use them to navigate the trickier sides (and angles) of geometric shapes.

Inverse 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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