If sec (theta)= -3 and tan (theta) > zero, what's the value of sin (theta)

Because the tangent is > 0 and the secant is < 0 , theta lies in the 3rd quadrant

The secant is -3/1 = 3 /-1 = r /x

The sine will be negative here and is given by :

- √ [ r^2 - x^2 ] / r = - √ [ (3)^2 - (-1)^2 ] / = - (√8 ) / 3