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?

Answered by Hannah M. Maths tutor

4770 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

[FP2] Solve: 3 cosh x - 4 sinh x = 7


By writing tan x as sin x cos x , use the quotient rule to show that d dx ðtan xÞ ¼ sec2 x .


1)Simplify sqrt 98 - sqrt 32, givimg your answer in the form k sqrt 2 where k is an integer.


How to differentiate y=(x^2+4x)^5


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences