Question

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

Answer 1

`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)`

Answer 2

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`