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Chapter 0: Problem 5

Convert each angle to radian measure. $$ -120^{\circ} $$

Short Answer

Expert verified
The angle \(-120^{\circ}\) in radians is \(-\frac{2}{3} \pi\).

Step by step solution

01

Write down the given angle and conversion factor

We are given the angle: \(-120^{\circ}\), and we know that \(1 radian = \frac{180}{\pi} degrees\).
02

Convert the angle to radians

To convert the angle from degrees to radians, we need to multiply the given angle in degrees by the conversion factor: \[-120^{\circ} \times \frac{\pi}{180^{\circ}}\]
03

Simplify

Now, we will simplify the expression by dividing -120 by 180 and multiplying the result by \(\pi\): \[-\frac{120}{180} \times \pi = -\frac{2}{3} \times \pi\]
04

Write the final answer

The angle \(-120^{\circ}\) converted to radians is: \[-\frac{2}{3} \pi\]

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Most popular questions from this chapter

Find \(f^{-1}(a)\) for the function \(f\) and the real number \(a\). $$ f(x)=\frac{3}{\pi} x+\sin x ; \quad-\frac{\pi}{2}

a. Plot the graph of \(f(x)=\cos (\sin x)\). Is \(f\) odd or even? b. Verify your answer to part (a) analytically.

Plot the graph of the function \(f\) in (a) the standard viewing window and (b) the indicated window. $$ f(x)=x^{3}-20 x^{2}+8 x-10 ; \quad[-20,20] \times[-1200,100] $$

a. If \(f(x)=x-1\) and \(h(x)=2 x+3\), find a function \(g\) such that \(h=g \circ f\). b. If \(g(x)=3 x+4\) and \(h(x)=4 x-8\), find a function \(f\) such that \(h=g \circ f\).

Find the inverse of \(f .\) Then use a graphing utility to plot the graphs of \(f\) and \(f^{-1}\) using the same viewing window. $$ f(x)=1-\frac{1}{x} $$
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