Homework Help: Math - complex numbers

Posted by Chiquesta on Saturday, December 17, 2011 at 12:59am.

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

2. 5pi/32

3. 5pi/32

Could you please guide me through the solutions, thank you SO much :)

Math - complex numbers - drwls, Saturday, December 17, 2011 at 2:41am
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.
Math - complex numbers - Chiquesta, Saturday, December 17, 2011 at 3:36am
Sorry, yes I meant from 0 to pi/2 for the last two questions.

Answer this Question

Related Questions

precal - De Moivre’s theorem states, “If z = r(cos u + i sin u), then ...
precal - e Moivre’s theorem states, “If z = r(cos u + i sin u), then ...
trigonometry - Use De Moivre’s Theorem to simplify each expression. Write ...
trig - 6. Compute the modulus and argument of each complex number. I did a-c and...
precal - e Moivre’s theorem states, “If z = r(cos u + i sin u), then ...
calculus - Hi i need help for calcul with a Moivre's theorem: ( 1/2 ( -1 - i...
Math Calculus - The Image Theorem: The image theorem, a corollary of the ...
Math - I am in the 5th grade and my homework tonight is about complex numbers. I...
Calculus - two complex numbers Z and W are related by the formula W=(Z+1)/(1-Z) ...
calc - Verify that the function satisfies the three hypotheses of Rolle's ...

For Further Reading

First Name:
School Subject:
Answer: