If tan theta = -5/12 and sin theta is greater than or equal to 0 , determine 3sin theta - 2cos theta

This is a 2nd quad angle....hence the sine is positive....and since we have a 5-12-13 Pythagorean Triangle, the sine is just 5/13   ....so.....the cosine is -12/13

So.....

3sinΘ - 2cosΘ =

3(5/13) - 2(-12/13)  =

15/13 + 24/13 =

39/13