Question

PLZ HELP#VERYCONFUSED rewrite each expression in term with no power greater than 1

Answer 1

\[\cos ^{3}\]

Answer 2

cos^3theta

Answer 3

\[\cos ^{3}\theta \]

Answer 4

it is simply

\[\cos(\theta)\cos(\theta)\cos(\theta)\]

Answer 5

no i have to use like identities

Answer 6

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

Answer 7

but i have no idea how to do this

Answer 8

@zepdrix

Answer 9

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

Answer 10

yes i am sure but thanks

Answer 11

well start with

\[\cos(\theta) (\cos^2(\theta)) = \cos(\theta)(1 - \sin^2(\theta))\]

Answer 12

hmmm k

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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.

Answer 19

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!!!