Question

if sin x=.8 where x is an angle in the second quadrant , find the positive value of sin 1/2

Answer 1

\[\sin^{-1} (.8) = 53.13 degrees\] And since sin(x) is positive in the 1st and 2nd quadrants, then the law of sines says that sin(a) / A = sin(b) / B.
\[\sin(53.13) / .8 = \sin(.5) / B\]

Correct me if I'm wrong here.

Answer 2

The formula is for functions of half angle, so the formula would be sin 1/2 A = + or - square root of 1-cos A over 2