drasy22 2 years ago PLZ HELP#VERYCONFUSED rewrite each expression in term with no power greater than 1

1. drasy22

$\cos ^{3}$

2. drasy22

cos^3theta

3. drasy22

$\cos ^{3}\theta$

4. campbell_st

it is simply $\cos(\theta)\cos(\theta)\cos(\theta)$

5. drasy22

no i have to use like identities

6. drasy22

ex if it is sin ^4 u do sin2)^2 and then you put the identitiy for sin^2 and then solve

7. drasy22

but i have no idea how to do this

8. drasy22

@zepdrix

9. zepdrix

Hmm I'm not familiar with any identities that decrease the power on trig functions. Are you sure it wasn't suppose to be $$cos (3\theta)$$ ?

10. drasy22

yes i am sure but thanks

11. campbell_st

well start with $\cos(\theta) (\cos^2(\theta)) = \cos(\theta)(1 - \sin^2(\theta))$

12. drasy22

hmmm k

13. zepdrix

Oh I guess we could use the Half-Angle Formulas to decrease power. I somehow forgot about those when I made my last comment :) lol

14. zepdrix

Here's a helpful identity we can use. $\large \color{royalblue}{\cos^2x=\frac{1+\cos2x}{2}}$

15. drasy22

yeah u are right i will have to use the power reducing identities

16. drasy22

yeah i started by using that but i don't know what to do after that step

17. zepdrix

$\large \cos^3x\quad =\quad \cos x \color{royalblue}{\cos^2 x} \quad = \quad \cos x \color{royalblue}{\frac{1+\cos2x}{2}}$

18. zepdrix

Im not sure if that's exactly what you're looking for. But something to notice here is that we no longer even have a squared cosine, since the two cosines we're left with have different INSIDES, we can't combine them that way.

19. drasy22

yes i am looking for this but i think it is OK i will ask my teacher. but thanks both of u for ur help!!!