how do you find the reference angle of csc,sec, cot?

Question

for example: csc theta= 2 times square root of 3 / 2

Answer 1

Use a hand calculator or a table of trig function values.
If csc theta = 2 sqrt(3/2) = sqrt 6 = 2.44949.., then sin theta = 0.40825
theta = arcsin 0.40825 = 24.095 degrees

I used the "arcsin" or sin^-1 function on my HP hand calculator for the last step. I also used the "sqrt" function earlier.