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

1 Answer
Nghi N
Dec 21, 2016

+- 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

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