Trigonometry Flashcard Review: Evaluating Trig Functions

Front

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

Back

The range of the inverse sine function is \( [-\frac{\pi}{2}, \frac{\pi}{2}] \).

Front

What is the value of \( \sin^{-1}(-\frac{1}{2}) \)?

Back

The value of \( \sin^{-1}(-\frac{1}{2}) \) is \( -\frac{\pi}{6} \).

Front

What is the value of \( \arctan(-\frac{\sqrt{3}}{3}) \)?

Back

The value of \( \arctan(-\frac{\sqrt{3}}{3}) \) is \( -\frac{\pi}{6} \).

Front

How do you find the coterminal angle of \( 600^{\circ} \)?

Back

To find the coterminal angle, subtract \( 360^{\circ} \) from \( 600^{\circ} \): \( 600^{\circ} - 360^{\circ} = 240^{\circ} \).

Front

What is the value of \( \cos(600^{\circ}) \)?

Back

The value of \( \cos(600^{\circ}) \) is \( -\frac{1}{2} \).

Front

What is the definition of \( \csc^{-1}(x) \)?

Back

The \( \csc^{-1}(x) \) function is the inverse of the cosecant function, defined for \( x \) such that \( |x| \geq 1 \).

Front

What is the value of \( \csc^{-1}(-\sqrt{2}) \)?

Back

The value of \( \csc^{-1}(-\sqrt{2}) \) is \( -\frac{\pi}{4} \).

Front

What is the value of \( \cos^{-1}(\frac{\sqrt{3}}{2}) \)?

Back

The value of \( \cos^{-1}(\frac{\sqrt{3}}{2}) \) is \( \frac{\pi}{6} \).

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

What is the definition of the tangent function in terms of sine and cosine?

Back

The tangent function is defined as \( \tan(x) = \frac{\sin(x)}{\cos(x)} \).