Math - complex numbers
posted by Chiquesta .
These questions are related to de moivre's theorem:
z^n + 1/z^n = 2cosntheta
z^n - 1/z^n = 2 isin ntheta
1. Express sin^5theta in the form Asintheta + Bsin3theta + Csin5theta and hence find the integral of sin^5theta.
2. Express sin^6theta in multiples of costheta and hence evaluate the integral of sin^6theta between 0 and pi/2.
3. Evaluate the integral of cos^7theta between pi/2 and 0.
The answers are:
1. -1/80cos5theta + 5/48cos3theta - 5/8costheta
Could you please guide me through the solutions, thank you SO much :)
If you had posted one at I time, I could have helped with one of them. It is past my bedtime here.
When you say "between pi/2 and 0" do you mean from pi/2 to zero? That would be backwards.
Please be more specific.
Sorry, yes I meant from 0 to pi/2 for the last two questions.