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What is the derivative of Cos(x) when x is measured in degrees?.

Sagot :

Answer:

- sinx

Step-by-step explanation:

This is a standard derivative and applies to angles in degrees or radians.

[tex]\frac{d}{dx}[/tex] (cosx ) = - sinx

Hrishii

Answer:

[tex]\huge\purple{- \frac{\pi}{180}\sin \: \bigg( \frac{\pi x}{180}\bigg)}[/tex]

Step-by-step explanation:

[tex]x \degree = \frac{\pi x}{180} \\ \\ \implies \: \cos \: (x \degree) = \cos \:\bigg( \frac{\pi x}{180}\bigg) \\ \\ \implies \: \frac{d}{dx} \cos \: (x \degree) = \frac{d}{dx} \: \cos \: \bigg( \frac{\pi x}{180}\bigg) \\ \\ = - \sin \: \bigg( \frac{\pi x}{180}\bigg)\frac{d}{dx} \bigg( \frac{\pi x}{180}\bigg) \\ \\ = - \sin \: \bigg( \frac{\pi x}{180}\bigg) \bigg(\frac{\pi}{180}\bigg) \\ \\ \huge \red{= - \frac{\pi}{180}\sin \: \bigg( \frac{\pi x}{180}\bigg)}[/tex]

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