Inverse Trig (with Compositions)

Front

What is the RANGE of angles for inverse sine?

Back

[-\frac{\pi}{2}, \frac{\pi}{2}]

Front

Find the value of \(\sin(\arcsin(-\frac{1}{2}))\).

Back

\(\frac{1}{2}\)

Front

Find the value of \(\tan(\sin^{-1}(\frac{1}{2}))\).

Back

\(\frac{\sqrt{3}}{3}\)

Front

Find the value of \(\csc(\sin^{-1}(1))\).

Back

1

Front

Find the value of \(\cos(\sin^{-1}(\frac{-\sqrt{3}}{2}))\).

Back

\(\frac{1}{2}\)

Front

Define inverse sine (arcsin).

Back

The inverse sine function, \(\sin^{-1}(x)\), returns the angle whose sine is \(x\), with a range of \([-\frac{\pi}{2}, \frac{\pi}{2}]\).

Front

What is the relationship between sine and arcsine?

Back

If \(y = \sin(x)\), then \(x = \sin^{-1}(y)\) for \(y \in [-1, 1]\).

Front

What is the domain of the inverse sine function?

Back

The domain of \(\sin^{-1}(x)\) is \([-1, 1]\).

Front

What is the value of \(\sin(\frac{\pi}{6})\)?

Back

\(\frac{1}{2}\)

Front

What is the value of \(\tan(\frac{\pi}{6})\)?

Back

\(\frac{1}{\sqrt{3}}\) or \(\frac{\sqrt{3}}{3}\)