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Chapter 4: Problem 15

Convert each angle in degrees to radians. Express your answer as a multiple of \(\pi\). $$135^{\circ}$$

Short Answer

Expert verified
The angle \(135^{\circ}\) is equal to \(\frac{3\pi}{4}\) radians when expressed as a multiple of \(\pi\).

Step by step solution

01

Understand the Conversion Formula

Firstly, it must be remembered that the relationship between degrees and radians is provided by the formula \(1^{\circ} = \frac{\pi}{180} \) radians. This is how we can interconvert these two units of angle measure.
02

Apply the Conversion Formula

Next, multiply the given angle in degrees by the conversion factor. This is done by multiplying \(135^{\circ}\) by \(\frac{\pi}{180}\) to get the radian measure.
03

Simplify the Expression

Simplify the resulting fraction as follows: \(\frac{(135\pi)}{180} = \frac{3\pi}{4}\).

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Most popular questions from this chapter

Use a vertical shift to graph one period of the function. $$y=\sin x-2$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When I convert degrees to radians, I multiply by \(1,\) choosing \(\frac{\pi}{180^{\circ}}\) for 1

Use a graphing utility to graph two periods of the function. $$y=0.2 \sin \left(\frac{\pi}{10} x+\pi\right)$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I made an error because the angle I drew in standard position exceeded a straight angle.

Use a vertical shift to graph one period of the function. $$y=\cos x-3$$
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