Verify that the function x(\theta)= \frac{\pi}{180}\theta converts an angle from degrees to...


Verify that the function {eq}x(\theta)= \frac{\pi}{180}\theta {/eq} converts an angle from degrees to radians by plugging in {eq}\theta= 360^\circ. {/eq}

So {eq}\frac{d}{d\theta}(\sin(x(\theta)))= \frac{d}{d\theta}(\sin(\frac{\pi}{180}\theta)) {/eq} would tell us how the sine function is changing, per degree (rather than per radian). Determine {eq}\frac{d}{d\theta}(\sin(\frac{\pi}{180}\theta)). {/eq}

Measurement of Angle


An angle has two major units of measurement : degrees and radians.

1. Degrees : One revolution is divided into 360 parts called degrees.

2. Radians : One radian is defined as the angle enclosed by an arc of length equal to that of radius of circle. That is,

$$\displaystyle \theta \text{ (in radians)} = \frac{l}{r} \\ $$

The conversion between degrees and radians is given by :

$$\displaystyle 180 \ ^{\circ} = \pi \ radians \\ $$

Answer and Explanation: 1

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Given function for conversion from degrees to radians :

$$\displaystyle x(\theta) = \frac{\pi}{180} \theta \\ $$

Plugging the angle 360...

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Learn more about this topic:

Converting 1 Radian to Degrees


Chapter 22 / Lesson 25

In this lesson, we'll find the relationship between radians and degrees. We'll then use that relationship to convert 1 radian to degrees and extend this procedure to other examples.

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