Expert: Paul Klarreich - 1/26/2011

Question
I'm in grade 12 Trig & 3-space, and right now I'm working on trigonometric functions.

The question I have is:

Angle x is in the third quadrant and satisfies tan(x#=8/15. What is the value of sin#x)?


So, I've done a few of these before, but I'm not sure what to do with this one. I know that Tanx = sinx/cosx, but that doesn't seem to be helping me get anywhere with this question, any tips?

Answer
Questioner: Kim
Country: Canada
Category: Advanced Math
Private: No
Subject: Trig & 3-Space
Question: I'm in grade 12 Trig & 3-space, and right now I'm working on trigonometric functions.

The question I have is:

Angle t is in the third quadrant and satisfies tan(t)=8/15. What is the value of sin(t)?


So, I've done a few of these before, but I'm not sure what to do with this one. I know that Tanx = sinx/cosx, but that doesn't seem to be helping me get anywhere with this question, any tips?
.........................
Tip: do not use x for an angle.  It conflicts with the:

Definitions:

sin t = y/r

cos t = x/r

tan t = y/x

If tan t = 8/15, assign y = -8, x = -15. (You did say third quadrant, right?)

Now use the pythagorean theorem to get r, and you are on your way.