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How are the derivatives of sine and cosine related?

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Diagram of a right triangle labeled with sides a, b, and hypotenuse c, alongside formulas for the six trigonometric functions-sine, cosine, tangent, cosecant, secant, and cotangent-each defined by ratios of the triangle's sides. — trigonometry Based on the definitions, various simple relationships exist among the functions. For example, csc A = 1/sin A, sec A = 1/cos A, cot A = 1/tan A, and tan A = sin A/cos A.

In the context of calculus and trigonometry, the derivatives of the sine and cosine functions are closely related through their cyclical nature:

The derivative of $\sin x$ with respect to $x$ is $\cos x$ .1
The derivative of $\cos x$ with respect to $x$ is $- \sin x$ .2

This relationship demonstrates that differentiating these functions results in the other, with a sign change occurring when moving from the derivative of cosine to sine.21