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Problem 97 Hard Difficulty

Use the Chain Rule lo show that if $ \theta $ is measured in degrees, then
$ \frac {d}{d \theta} (\sin \theta) = \frac {\pi}{180} \cos \pi $
(This gives one reason for the convention that radian measure is always used when dealing with trigonometric functions in calculus: the differentiation formulas would not be as simple if we used degree measure.)

Answer

$\frac{\pi}{180} \cos \theta^{\circ}$

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Video Transcript

Okay, so we typically working radiance and calculus. But what if we decided to work in degrees? We know that fate a radiance is equal to pi over 1 80 tons x degrees. So if we had the function y equals sine data, we could think of it as why equals the sign of pi over 1 80 times X. Now, suppose we wanted to find its derivative. We would need to use the chain rule. The derivative of the outside would be co sign so we would have co sign of pi over 1 80 times X times the derivative of the inside and the derivative of the inside would be pi over 1 80 Now, if we went back and placed the pi over 1 80 in the beginning of the expression and then if we substituted Fada back in here for pi over 1 80 times X, we would have pi over 1 80 times a co sign of data. So this is much more complicated as a derivative than if we just use radiance