Question

Find soltuions; 7 sin^2 x 14 sin x + 2 = -5

Answer 1

I've had a very generous user walk me though a previous question but I'm not sure how different it is when dealing with an equation with a -7 at the end

Answer 2

Is there supposed to be a plus sign between the sin^2 x and the 14?

Answer 3

yeah, lol sorry

Answer 4

no, a negative sign actually

Answer 5

No problem... this one is of the form \[ax ^{2}+bx+c=0\]we just have to get it there.
I would start by bringing that -5 over which will set the whole thing to zero.

Answer 6

There is a very nice simplification here.... divide everything by 7 to simplify.

Answer 7

Then use a substitution for sin x . I think that you mentioned that you would use a (I use u).

Answer 8

7sin(sin x -2)-3=0 or sin^2 x - 2sin -3 =0?

Answer 9

The second one

Answer 10

but not quite

Answer 11

when you bring the five over... you should add 5 to both sides... 2+5 is 7... 7/7 is one.

Answer 12

I see, you're right, I subtracted disregardling the sign change when carrying over. So we would plug "sin^2 x - 2sin + 1 = 0 into a graphing calculator and observe the intervals for the solutions?

Answer 13

You could see the x-intercepts (which are the solutions) that way. But generally we use algebra style factoring to get to the next part. If I say a=sinx, they your problem becomes\[a ^{2}-2a+1=0\]

Answer 14

They didn't appear to give you an interval over which these solutions exist, so we will assume that the interval is \[(-\infty,\infty)\]

Answer 15

Oh, wow, you're right. If that's the case then it isn't really necessary to use a calculator since the lines are constant, right?

Answer 16

That tangent problem was tricky... I just used the calculator to better visualize what was going on. If you can see this stuff in your head, the calculator is not needed. This problem is simpler than the last.

Answer 17

lol I think it's safe to say that was a trick question. My teacher is notorious for those. Thanks again, you've been a lot of help. Good night =)

Answer 18

No problem, good night.