You are Here: Home >< Maths

# Can somebody clear up some trig differentiation/integration watch

Announcements
1. I am a little confused with:

d/dx sin2x

d/dx cos2x

d/dx sin3x

d/dx sin^2(x)

d/dx cos^2(x)

and the respective integrals, could somebody be kond enough to clear this up for me, many thanks in advance.
2. (Original post by rayman198)
I am a little confused with:

d/dx sin2x

d/dx cos2x

d/dx sin3x

d/dx sin^2(x)

d/dx cos^2(x)

and the respective integrals, could somebody be kond enough to clear this up for me, many thanks in advance.
The first 3 can be done by the chain rule.

Let u=2x
d/dx(sin2x) = d/du(sinu).du/dx
= 2cosu
= 2cos2x

and the same goes for the other two; -2sin2x and 3cos3x

to integrate them, you need to divide by the constant multiplying x rather than multiply by it.

eg. INT sin2x dx = -0.5 cos 2x

which you can verify by differentiation.

cos^2(x) and sin^2(x) can be differentiated using the chain rule.
let u = sinx
d/dx(u^2) = 2u du/dx
= 2sinx cosx

To integrate them, use the double angle formula cos2x = 1-2sin^2(x) = 2cos^2(x) - 1
and re-arrange to get cos^2(x) = 0.5 (1+cos2x) and sin^2(x) = 0.5 (1-sin2x)

and you integrate as above.
3. thanks for tha, you should be a teacher (if you arent already) il owe that extra 10% in my exam tomorrow to you!
4. Generally

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: June 11, 2006
Today on TSR

And I hate it

### University open days

• Manchester Metropolitan University
Wed, 14 Nov '18
• University of Chester
Wed, 14 Nov '18
• Anglia Ruskin University
Ambitious, driven, developing your career & employability? Aspiring in your field, up-skilling after a career break? Then our Postgrad Open Evening is for you. Postgraduate
Wed, 14 Nov '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams