How can I remember how to differentiate and integrate cos and sin?

I find it is best whenever you open your maths paper to draw this diagram to help you remember: Sin(X) -> cos(X)-> -sin(X) -> -cos(X)----->
{Drawn in a circle on the board}
To differentiate you follow the circle clockwise from sine you get cosine but when you differentiate cosine there is a sign change and we get minus sine.
Also it is important to remember that if there is a coefficient, like:
Y= Cos(2x)
We have to times by this when we differentiate and divide by it when we integrate:
dY/DX= 2cos(2x) Integral(Y) = 1/2 cos(2x).
{Symbols drawn on board}
Shall we try some examples?

HM
Answered by Hannah M. Maths tutor

5574 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Using answer to previous question state the coordinates of the minimum


How do you integrate y = 4x^3 - 5/x^2?


A girl kicks a ball at a horizontal speed of 15ms^1 off of a ledge 20m above the ground. What is the horizontal displacement of the ball when it hits the ground?


f(x)=12x^2e^2x - 14, find the x-coordinates of the turning points.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning