Question

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

Answer 1

`\huge\purple{- (\pi)/(180)\sin \: \bigg( (\pi x)/(180)\bigg)}`

Explanation:

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

Answer 2

- sinx

Explanation:

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

`(d)/(dx)` (cosx ) = - sinx