What is an easy way to remember how sin(x) and cos(x) are differentiated and integrated?

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If you imagine that sin(x), cos(x), -sin(x) and -cos(x) are on a wheel as shown below:

      sin(x)

-cos(x)  cos(x)

     -sin(x)

then going clockwise around the wheel you have what each term differentiates to, so sin(x) to cos(x), cos(x) to -sin(x) etc, and anticlockwise you have what each term integrates to, so sin(x) to -cos(x), -cos(x) to -sin(x) etc etc. 

Hannah E. A Level Maths tutor

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