If csc ( x ) = 13/12 (in Quadrant-I), find sin ( 2 x ) =

Question

If csc ( x ) = 13/12 (in Quadrant-I), find sin ( 2 x ) =

Answer 1

sin2x = 120/169

cscx = 1/sinx = 13/12, so sinx = 12/13, cosx = 5/13. It's a 5-12-13 right triangle

sin2x = 2sinxcosx = 2(12/13)(5/13) = 120/169 = about 0.71

2x = sin-1(0.71) = about 45.24 degrees

x = 45.24/2 = 22.62 degrees