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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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