Question in trigonometry

  • #1
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! :smile:
 

Answers and Replies

  • #3
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.
 
Last edited:

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