Evaluating Trig and Inverse Trig

Front

What is the range of the inverse cosine function, \( \cos^{-1}(x) \)?

Back

The range of the inverse cosine function is \([0, \pi]\).

Front

Evaluate \( \cos^{-1}\left(\frac{\sqrt{3}}{2}\right) \).

Back

\( \frac{\pi}{6} \) or 30°.

Front

What is the value of \( \csc(120°) \)?

Back

\( \frac{2\sqrt{3}}{3} \) or approximately 1.155.

Front

Evaluate \( \sin^{-1}\left(\frac{\sqrt{2}}{2}\right) \).

Back

\( 45° \) or \( \frac{\pi}{4} \).

Front

What is the value of \( \sin^{-1}(-1) \)?

Back

\( -\frac{\pi}{2} \) or -90°.

Front

What is the relationship between sine and cosecant?

Back

Cosecant is the reciprocal of sine: \( \csc(x) = \frac{1}{\sin(x)} \).

Front

What is the value of \( \sin(90°) \)?

Back

1.

Front

What is the value of \( \cos(0°) \)?

Back

1.

Front

What is the value of \( \tan(45°) \)?

Back

1.

Front

What is the domain of the inverse sine function, \( \sin^{-1}(x) \)?

Back

The domain of the inverse sine function is \([-1, 1]\).