I'm trying to do my math homework,but I got stuck in this problem.

Find the other trigonometric functions values if $\sin{x}=\frac{5}{13}$ and $\tan{x}<0$.

If $x$ would have been given in only one quadrant it would be fine but here $\tan{x}<0$ in the second and fourth quadrants.

When I find $\cot{x}$ it's easy because it has the same sign in both given quadrants, but how to find $\cos{x}$ when we know that $\cos$ in the second quadrant is negative and in the fourth quadrant is positive?

Thank you!

  • 2
    $\begingroup$ But you know the sign of the sine, so that determines the quadrant. $\endgroup$ Sep 24 '13 at 19:33
  • $\begingroup$ Yes exactly now I understand it.Thank you very much! $\endgroup$
    – Student
    Sep 24 '13 at 19:36
  • 1
    $\begingroup$ Panarit: We highly encourage users to accept an answer when they find one to be helpful. You can accept one answer per question. To accept an answer, click on the $\large \checkmark$ to the left of the answer you'd like to accept. You get two reputation points for each question/answer accepted. You also have enough reputation now to upvote helpful answers, and you can upvote (click on $\uparrow$ so it turns red) every answer you find helpful! $\endgroup$
    – amWhy
    Sep 30 '13 at 15:05


As $$\tan x=\frac{\sin x}{\cos x},\cos x=\frac{\sin x}{\tan x}$$

We have $\sin x>0,\tan x<0$


$$\text{Knowing}\;\;\sin x = \frac 5{13} > 0, \;\text{ then }\; \tan x = \dfrac {\sin x}{\cos x} \lt 0 \implies \cos x \lt 0$$

In which quadrant is $\sin x > 0, \cos x \lt 0$?


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