Question

If cot(theta)=1.5 and theta is in quadrant 3, what is the value of sin theta

Answer 1

The answer:
cot(theta)=1.5, to find theta, cot(theta)=1.5 implies theta= arc cot (1.5)

but we kknow that cot(theta) = 1 /  tan(theta), this implies 

 1 /  tan(theta) =1.5, and  tan(theta) = 1 / 1.5 = 0.6
 
and theta is in quadrant 3,  costheta and sintheta are negatives

so  tan(theta) is positive, 

tan(theta) = 0.6, therefore,  (theta) = arctan ( 0.6)= 30.9°

finally  (theta) =  30.9°