need help finding a tangent please

[corsec]

I'm not exactly sure how to go about this problem

tan theta =

sin theta
-----------
cosine theta

if I have those two or any form of those two I can get tangent however what do I do when I get this

given sin theta = 7/13 and tan theta is < 0 find tan theta

conversely

given cos theta = -7/13 through time pi/2 < theta < pi find tan theta

real confused on how to do this

 

[royhaas]

Use the identity \(\displaystyle sin^2(\theta)+cos^2(\theta)=1\). along with the information on which quadrant(s) the angle must lie.

 

[corsec]

i think i see what your saying but i'm not exactly sure how to apply that approach

 

[stapel]

Draw the right triangle. Label the base angle "theta". Using the signs on the sine and tangent functions, determine the quadrant. Using the given side lengths (from the sine ratio) and the Pythagorean identity, find the value of the third side. Make sure to take the signs in that quadrant into account.

Now read off the value of the tangent from your triangle.

Eliz.