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Chapter 0: Problem 8

Convert each angle to radian measure. $$ -495^{\circ} $$

Short Answer

Expert verified
The angle \(-495^{\circ}\) is equal to \(\dfrac{-11\pi}{4}\) radians.

Step by step solution

01

Identify the angle in degrees

The given angle is \(-495^{\circ}\).
02

Use the conversion factor to convert the angle to radians

Multiply the given angle by the conversion factor \(\frac{\pi}{180}\): \[ -495^{\circ} \times \frac{\pi}{180} \]
03

Perform the calculation and simplify

Now, we will multiply and simplify: \[ \frac{-495\pi}{180} \] To simplify the fraction, we can divide both the numerator and denominator by common factors. In this case, the highest common factor is 45: \[ \frac{-11\pi}{4} \]
04

Write the final answer in radian measure

The angle \(-495^{\circ}\) is equal to \(\dfrac{-11\pi}{4}\) radians.

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Most popular questions from this chapter

Sketch the graph of the first function by plotting points if necessary. Then use transformation(s) to obtain the graph of the second function. \(y=\cos x, \quad y=\frac{1}{2} \cos \left(x-\frac{\pi}{4}\right)\)

Sketch the graph of the first function by plotting points if necessary. Then use transformation(s) to obtain the graph of the second function. \(y=x^{2}, \quad y=x^{2}-2\)

Find the zero(s) of the function f to five decimal places. $$ f(x)=2 x^{3}-3 x+2 $$

Show that \(f\) and \(g\) are inverses of each other by verifying that \(f[g(x)]=x\) and \(g[f(x)]=x\). $$ \begin{aligned} &f(x)=4(x+1)^{2 / 3}, \text { where } x \geq-1 \\ &g(x)=\frac{1}{8}\left(x^{3 / 2}-8\right), \text { where } x \geq 0 \end{aligned} $$

Find \(f^{-1}(a)\) for the function \(f\) and the real number \(a\). $$ f(x)=2 x^{5}+3 x^{3}+2 ; \quad a=2 $$
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