SOLUTION: If tan θ = -4/3 and sin θ > 0, find the exact value of cos θ. I have no idea how to do this, so please show me how.

You have  =  and  > 0.

It means that the angle  is in QII, second quadrant.


Further, the tangent is the ratio of two legs in an right angled triangle.
In your case the legs are 4 and 3 units long.


Did you ever hear about (3,4,5) right angled triangle ?


Its hypotenuse is 5 units.   Every 4-grade student knows it.


Then  is , the ratio of the longer leg to the hypotenuse, 
and since the angle is in QII, the cosine is negative.  Which gives you the


Answer.   = .