Question

what steps would I take to solve the problem:
Solve each equation on the interval 0 10 years ago

Answer 1

Do you mean \(0<x<2\pi\) or do you mean \(0 < \alpha < 2\pi\)?

Answer 2

the 2nd one

Answer 3

But there are no alphas in your problems...

Answer 4

that why im confused as well lol
maybe it is the first one

Answer 5

Let's just assume that it is the first one, because that would make more sense lol

Answer 6

So, for the first one.\[2\sin(x)+\sqrt{2}=0\]\[2\sin(x)=-\sqrt{2}\]\[\sin(x)=-\frac{\sqrt{2}}{2}\]Now, use your trig tables to find what values of x satisfy that while making sure \(0 < x < 2\pi\). Get it?

Answer 7

oh so you pretty much want to get the sin alone

Answer 8

what if there is sin and cos in the problem.
ex:8-12sin^2x=4cos^2x

Answer 9

Yeah. When solving trig equations, you want to (1) get all the trig stuff into 1 trigonometric function. So, if you have both a sine and a cosine or something, you want to (usually) get it all in terms of sine or cosine. (2) You want to solve for the trig function.

Answer 10

For that kind of thing, that's where you have to use your identities. For instance, in that question you just posted, trying using your pythagorean identities.
\[\implies8 - 12\sin^2(x)=4\cos^2(x)\]\[\implies8-12\sin^2(x)=4(1-\sin^2(x))\]\[\implies0=8\sin^2(x)-4\]\[\implies\frac12=\sin^2(x)\]Does this make sense?

Answer 11

ahh yes I finally understand :D
thanks so much!

Answer 12

You're welcome. :)