SOLUTION: 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

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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
Found 2 solutions by Boreal, MathTherapy:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
I would go the other way
csc=2 sqrt(3)/3 is 2/sqrt(3)
Therefore the sin is sqrt (3)/2
That occurs at pi/3 and 2pi/3 on the interval 0 to 2 pi (which covers the above.
With the calculator, try entering 3/(2sqrt(3))
You should get 0.8660.
if you enter 3/2 sqrt(3), the calculator will make that 1.5 *sqrt(3), and you can't take the arc sin of it, because it is greater than 1.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
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
You're on the right track, but need guidance.

You're correct in that: . However, you MUST RATIONALIZE the denominator. 

We then get:  =====>  =====>  =======>  ======> 

Now, this is the answer since the EXACT value is required, and since , 

then  is in the 2nd quadrant, where sin is positive (> 0) 

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