What is d/dx(sin x^ ), with x in degrees?

Question 22

MediumOriginal question

What is $\frac{d}{dx}\left(\sin x^{\circ}\right)$ , with $x$ in degrees?

\cos x^{\circ}

Correct answerYour answer

\frac{180}{\pi}\cos x^{\circ}

Correct answerYour answer

\frac{\pi}{180}\cos x

Correct answerYour answer

\frac{\pi}{180}\cos x^{\circ}

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Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$x^{\circ} = \frac{\pi x}{180}$ radians, so $\sin x^{\circ} = \sin\frac{\pi x}{180}$ .
Chain rule: $\cos\frac{\pi x}{180} \cdot \frac{\pi}{180} = \frac{\pi}{180}\cos x^{\circ}$ .

Worth noting

$\cos x^{\circ}$ uses the radian rule $\frac{d}{dx}\sin x = \cos x$ on an angle in degrees, losing the factor $\frac{\pi}{180}$ .

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