Question 1040321
Given csc theta = (2 sqr3)/(3) and -270 less than 0 less than 180
determine the exact values of theta

my work:

(2 sqr3)/3 = 1/sin theta
sin theta * (2sqr3)/3 =1
sin theta = 1/ (2sqr3/3)
sin theta = 3/ (2sqr3)
when I try to find the inverse of sin theta to find the angle, it gives me an error
<pre>You're on the right track, but need guidance.
You're correct in that: {{{sin (theta) = 3/(2sqrt(3))}}}. However, you MUST RATIONALIZE the denominator. 
We then get: {{{sin (theta) = 3sqrt(3)/(2sqrt(3) * sqrt(3))}}} =====> {{{sin (theta) = 3sqrt(3)/(2 * 3)}}} =====> {{{sin (theta) = 3sqrt(3)/6}}} =======> {{{cross(3)sqrt(3)/2cross(6)}}} ======> {{{sin (theta) = sqrt(3)/2}}}
Now, this is the answer since the EXACT value is required, and since {{{matrix(1,3, - 270 < theta < 180, "=", 90^o < theta < 180^o)}}}, 
then {{{sin (theta) = sqrt(3)/2}}} is in the 2nd quadrant, where sin is positive (> 0)