Finding the Exact Values of sinx and cosx in Trigonometric Equations

[glass.shards]

If tan2x=(-24/7), find the exact value(s) of sinx and cosx


Working out the answers by hand, I get

sinx = ±3/5, ±4/5
cosx = ±3/5, ±4/5


But by actually calculating x and plugging it into sinx and cosx, I get

sinx = 3/5, 4/5
cosx = 3/5, -4/5


I'm pretty sure that the latter are the answers, but how do I justify it given the ±?

Thanks!

 

[nanoWatt]

I believe that tan x = (sin x) / (cos x)

Is that the formula you are using?

I found it here: http://www.clarku.edu/~djoyce/trig/identities.html

 

[glass.shards]

Here's what I did:

tan2x = -24/7

so to find cosx and sinx, I established that on a graph:
y = -24
x = 7
r = 25

OR

y = 24
x = -7
r = 25

Thus, cos2x = ±7/25. By breaking down cos2x into (1-2(sinx)^2) and (2(cosx)^2-1) and working out the answers, I got four values, as listed in my previous post.

EDIT: Sorry, I meant eight values, counting the ±'s. I'm supposed to get four.