A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
PLZ HELP#VERY CONFUSED
rewrite each expression in term with no power greater than 1 cos^3 theta
anonymous
 3 years ago
PLZ HELP#VERY CONFUSED rewrite each expression in term with no power greater than 1 cos^3 theta

This Question is Open

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0The only way I can think of doing this is using complex numbers. Using Euler's formula we know that:\[\cos \theta =\frac{e^{i\theta}+e^{i\theta}}{2}\]Therefore:\[\cos^3\theta=\left(\frac{e^{i\theta}+e^{i\theta}}{2}\right)^3\]\[=\frac{1}{2^3}\left(e^{3i\theta}+3e^{2i\theta}e^{i\theta}+3e^{i\theta}e^{2i\theta}+e^{3i\theta}\right)\]\[=\frac{1}{2^3}\left(e^{3i\theta}+3e^{i\theta}+3e^{i\theta}+e^{3i\theta}\right)\]\[=\frac{1}{2^3}\left(e^{3i\theta}+e^{3i\theta}\right)+\frac{3}{2^3}\left(e^{i\theta}+e^{i\theta}\right)\]\[\frac{1}{4}\left(\frac{e^{3i\theta}+e^{3i\theta}}{2}\right)+\frac{3}{4}\left(\frac{e^{i\theta}+e^{i\theta}}{2}\right)\]Using Euler's formula again backwards yields:\[=\frac{1}{4}\cos 3\theta+\frac{3}{4}\cos \theta\]
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.