Question

How do you solve an equation with both sin and cos in it?

Answer 1

substitute for one of them

Answer 2

how?

Answer 3

there are no identities for just plain sin or cos

Answer 4

Why don't you post the equation and we'll take a look at it.

Answer 5

2sinx = cos3x

Answer 6

thankyou

Answer 7

\[2\sin x=\cos (2x+x)=\cos 2x \cos x-\sin 2x \sin x=(\cos ^2x-\sin ^2x)\cos x-2\sin x \cos x \sin x\]

Answer 8

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

Answer 9

\[(1-2\sin ^2x)\cos x-2\sin ^2x \cos x=\cos x(1-4\sin ^2x)\]

Answer 10

I'm afraid you lost me a little... could you explain what you did in words?
Just because I have a test on it tomorrow, and I don't think I could come up with this on my own

Answer 11

I wrote 3x as 2x+x and then used the cos(x+y) identity

Answer 12

Ahh ok, thanks! What is the cos(x+y) identity? I must have missed that one in my list

Answer 13

cos(x+y)=cosxcosy-sinxsiny

Answer 14

Oh wow I've never learned that one. Thank you so much!

Answer 15

yw. If you never had it, it probably won't be on the test. That is cos 3x and not cos^3x isn't it?

Answer 16

Yes! Hopefully my teacher won't have it on the test - I doubt it! Thanks again :) Last thing, if you have another minute, how would you solve an equation like cos x = 2x ?

Answer 17

It seems like it should be so easy, but I can't figure out where to start

Answer 18

The simpliest fastest way would be to graph y = cos x and the line y = 2x and identify the points of intersection. Will you be able to use a graphing calculator on your test?

Answer 19

Oh! Yes I can! That's perfect, thanks!

Answer 20

Then take the same approach with the other one you posted. Graph y = 2sinx and y

Answer 21

y= cos(3x) and identify the points of intersection.

Answer 22

Ahh that makes perfect sense! Yaayy:) Would I type it as sin ^-1, or just as sin?

Answer 23

Just like I stated it.

Answer 24

Will you have internet access during the test?

Answer 25

No, but we'll have our graphing calculators. But the graph isn't showing up on my calculator right now...

Answer 26

You probably need to adjust the range of values on the x or y axis or both.

Answer 27

Hmm I tried that. I have both the x and the y set at minimum -200 and maximum 200

Answer 28

Can you do radians on the x axis?

Answer 29

How do you mean?

Answer 30

So you don't know what radians means so just go from -10 to 10 on the x and -10 to 10 on the y

Answer 31

Yahooo! Got it :)

Answer 32

Thank you so much for your time! That was wonderfully helpful

Answer 33

More helpful than my notes, my textbook, and all my friends.. I suppose I just needed a nice clear answer

Answer 34

Excellent. Glad to help.