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Derivative of sin x

ddx[sin⁡(x)]=cos⁡(x)\frac{d}{dx}\left[\sin\left(x\right)\right] = \cos\left(x\right)

The slope of sine traces out cosine: steepest (slope 1) where sin x crosses zero going up, flat where sine peaks. This only works in radians; in degrees an extra factor of π/180 appears.

Derivation

  1. Trig rule

    ddx[sin⁡(x)]=cos⁡(x)\frac{d}{dx}\left[\sin\left(x\right)\right] = \cos\left(x\right)
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  • f(x) = sin x
  • f′(x)

Drag the graph · at x = 1.20 the slope is 0.36236, the height of the dashed curve.

Open in the derivative calculator

Questions students ask

What is the derivative of sin x?

ddx[sin⁡(x)]=cos⁡(x)\frac{d}{dx}\left[\sin\left(x\right)\right] = \cos\left(x\right).

How do you find the derivative of sin x?

The slope of sine traces out cosine: steepest (slope 1) where sin x crosses zero going up, flat where sine peaks. This only works in radians; in degrees an extra factor of π/180 appears.

What is the integral of sin x?

See the integral of sin x page for the antiderivative with steps.