Question

Using Power reduction to solve cos^4t dt?

Answer 1

Invalid question.

Answer 2

?

Answer 3

invalid?

Answer 4

@Isaiah.Feynman its cos^4 (t)

Answer 5

So what do you want to solve there?

Answer 6

well we have to use power reduction. wouldnt you reduce it to cos^2(t) cos^2(t)?

Answer 7

Yeah.

Answer 8

then(1+cos2x/2)(1+cos2x/2) ?

Answer 9

Where did you get that from?

Answer 10

cos^2x dx= integral of 1+cos2x/2

Answer 11

No. What you mean is the trig identity \[\cos^{2}x = 1-\sin^{2}x\]

Answer 12

its a power reduction formula?

Answer 13

No.

Answer 14

You could use the ummmm Half-Angle Formula's a bunch of times.

Or you could use the Cosine Redux Formula:\[\Large I_n\quad=\quad \frac{1}{n}\cos^{n-1}x \sin x +\frac{n-1}{n}I_{n-2}\]

Answer 15

Where I_n is,\[\Large I_n\quad=\quad \int\limits \cos^n x\;dx\]

Answer 16

Although, if you haven't learned about that yet, then maybe half-angles are easier :)

Answer 17

\[\Large \cos^4x \quad=\quad [\cos^2x]^2 \quad=\quad \left[\frac{1}{2}(1+\cos2x)\right]^2\]

Answer 18

Gotta expand that out and do some more half angle after that ^^

Answer 19

1/4(x+1/2sin2x)?

Answer 20

Hmm I'm confused.. did you ignore the square on the outside? D:

Answer 21

wouldnt it just be another 1/2?

Answer 22

No :(

Answer 23

hahaha. sorry. I dont really understand half angles

Answer 24

This is what expanding the brackets gives us,\[\Large \frac{1}{4}(1+2\cos2x+\cos^22x)\]That part make sense? :o

Answer 25

I multiplied out the outer square

Answer 26

ohhh i know this. duh

Answer 27

What is that reindeer doing on that lady's face? +_+
That's kinda rude.

Answer 28

You'll want to apply the Half-Angle Formula again to this orange term before you can integrate.
\[\Large \frac{1}{4}(1+2\cos2x+\color{orangered}{\cos^22x})\]

Answer 29

Doing reindeer things :D

Answer 30

pshhh

Answer 31

hmm so youd plug in the 1+cos2x/2 into it?

Answer 32

No the angle `doubles` each time we apply the rule.
So we multiply another 2 inside of the cosine.

Answer 33

\[\Large \cos^22x\quad=\quad \frac{1}{2}(1+\cos(2\cdot2x)) \quad=\quad\frac{1}{2}(1+\cos4x)\]
Understand how that works? :)
Dubs. The. Angle.

Answer 34

yup! thanks<3

Answer 35

@skay your smartscore graph is a straight line. Can you get it's equation? :P