Question

Find tan θ if cos θ = 12/13 and sin θ<0

Answer 1

use the identities sin^2+cos^2=1 and tan=sin/cos
I think there's a pythagorean triple with 2 sides 12 and 13. I forget the other side.

Answer 2

Remember SOH CAH TOA

You're given cos theta = 12/13 which is the CAH which means cosine is adjacent over hypotenuse.

See what I did there? You now can use the pythagorean theorem to find that other side, which is what sine and tangent are found using SOH and TOA. Good luck!

Answer 3

use my way if you like algebra more. use kainui's way if you like geometry more.

Answer 4

Tan theta=5/12 since cos theta=Adj/hyp

Answer 5

@KIEMA I'm getting -5/12, is this correct?

Answer 6

@Peter14 thank you very much!

Answer 7

jaytag is right, sin theta is less than zero