Question

find the exact value of each of the remaining trigonometric function of theta
tan theta = 5/12, cos theta < 0

Answer 1

Hint: \(\rm tan(t)=sin(t)/cos(t)\)
and \(\rm sin^2(t)+cos^2(t)=1\)

Answer 2

and \(\rm 1+tan^2(t)=1/cos^2(t)\)
This last one will make the work easier, and you won't need the first two identities.

Answer 3

Remember that Tan is y/x. In the problem, it states that the cos is less than zero, thus we conclude that the x must be negative. If the cosine is negative but tan is positive then the angle must fall in the 3rd quadrant. This results y = -5 and x = -12. Now we use a^2 = -5^2 + -12^2, which equals 13. Now we can write the cosine as -12/13