How do you find arcsin(-1/2) ?

2 Answers
Jun 22, 2018

arc sin(-1/2)=-pi/6

Explanation:

We know that,

color(red)((1)arc sin(-x)=-arc sinx

color(blue)((2)arc sin(sintheta)=theta ,theta in[-pi/2,pi/2]

Now,

arc sin(-1/2)=-arc sin(1/2)...tocolor(red)([Apply(1)]

arc sin(-1/2)=-arc sin(sin(pi/6))to[because sin(pi/6)=1/2]

arc sin(-1/2)=-pi/6...tocolor(blue)(Apply(2)

Jun 23, 2018

arc x = (7pi)/6
arc x = (11pi)/6

Explanation:

sin x = - 1/2
Trig table and unit circle give 2 arcs x that have the same sin value (-1/2):
x = - pi/6, or x = (11pi)/6 (co-terminal), and
x = pi - (-pi/6) = (7pi)/6