Let theta be an angle in standard position. If the point (a,5) lies on the terminal side of theta and csc(theta)=sqrt(13)/2, what is a?

Answer 1

cscx = sqr13/2 = hypotenuse/opposite side

sinx = 1/cscx = 2/sqr13 = opposite side/hypotenuse

cosx = sqr(13-4)/sqr13 = sqr9/sqr13 = 3/sqr13 = adjacent side/hypotenuse with

(3,2) lying on the terminal side of theta (x). to get to (a,5) with the same angle would mean 3/2 = a/5 and a= 15/2 = 7 1/2