Trig question

  • #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 ±?
 

Answers and Replies

  • #2
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 those four values.
 
  • #3
Gib Z
Homework Helper
3,346
6
You get extra false solutions from taking both positive and negative values from the square root. The only way to justify the latter answers is to verify each of the possibilities and saying some did not evaluate to the correct value.
 

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