Question

How do you solve and find the value of `sin(2sin^-1(1/2))`?

Answer 1

`+- sqrt3/2`

Explanation:

`sin (2sin^-1 (1/2)) --> sin (2arcsin (1/2))`
Trig table and unit circle give:
`sin x= 1/2` --> arc `x = pi/6` and arc `x = (5pi)/6`

a. `sin 2x = sin (2(pi)/6) = sin (pi/3) = sqrt3/2`
b. `sin 2x = sin (2(5pi)/6) = sin ((5pi)/3) = - sin (pi/3) = - sqrt3/2`
Finally:
`sin (2sin^-1 (1/2)) = +- sqrt3/2`