Question

Find the exact value of sin-1 the quantity square root of three divided by two.

a. three pi divided by four
b. pi divided by three
c. two pi divided by three
d. pi divided by four

Answer 1

Option b is correct.

Exact value of
`\sin^(-1)((√(3) )/(2))` is; pi divide by 3

Explanation:

To find the exact value of
`\sin^(-1)` the quantity square root of three divided by two.

square root of three means
`√(3)`

Two means 2

The quantity square root of three divided by 2 is;
`(√(3) )/(2)`

Given:
`\sin^(-1)((√(3) )/(2))`

Let
`\sin^(-1)((√(3) )/(2))` = y

Taking sine both sides we get;

`\sin(\sin^(-1)((√(3) )/(2))) = \sin y`

Simplify:

`\sin y = (√(3))/(2)`

We know that the value of
`\sin 60^(\circ) = (√(3) )/(2)`

`\sin y = (√(3))/(2)` =
`\sin 60^(\circ)`

On comparing we have;

`y = 60^(\circ) =(\pi)/(3)`

Therefore, the exact value of
`\sin^(-1)((√(3) )/(2))` is;
`(\pi)/(3)`