These are the factor formulas:
I have an exam tomorrow but the questions which will come up I have never come across before. Some of the questions involve the Factor Formulae which I have never seen before so I was wondering whether you might give some examples and perhaps links to other pages where I can take a long revision.
1. Using the factor formulae evaluate the integrals of the type (sinx cos3x)dx
2. Use the factor formulae to prove trig identities.
I have a general understanding of Trigonometry and I have just completed my Calculus.
We've just been told today about this exam and I have no idea how the factor formulae looks like and how to use it.
Here is an example which I have been able to finish using the factor formulae that I found.
Prove that: 4(cosx + cos2x)sin3xsinx = cos4x - cos8x
=2(cosx + cos2x) 2sin3xsinx
Reverse using factor formulae
=2(cosx + cos2x)(cos4x - cos2x)
From here I know I am wrong because I have tried it all the way and the outcome is wrong.
So no one understands the factor formulae? If I could learn how to integrate this: (sinx cos3x)dx using the factor formulae that would be great, because I have done some research on proving trig using the factor formulae and revise enough.
We change the integral into sum of two sines as above using the factor formulas. Then we use the chain rule to integral each one separately...
The outcome will be:
3/2cos(x+3x) + -3/2cos(x-3x) +c
Is that right?