Respuesta :
Answer:
Option b is correct.
Exact value of [tex]\sin^{-1}(\frac{\sqrt{3} }{2})[/tex] is; pi divide by 3
Step-by-step explanation:
To find the exact value of [tex]\sin^{-1}[/tex] the quantity square root of three divided by two.
square root of three means [tex]\sqrt{3}[/tex]
Two means 2
The quantity square root of three divided by 2 is; [tex]\frac{\sqrt{3} }{2}[/tex]
Given: [tex]\sin^{-1}(\frac{\sqrt{3} }{2})[/tex]
Let [tex]\sin^{-1}(\frac{\sqrt{3} }{2})[/tex] = y
Taking sine both sides we get;
[tex]\sin(\sin^{-1}(\frac{\sqrt{3} }{2})) = \sin y[/tex]
Simplify:
[tex]\sin y = \frac{\sqrt{3}}{2}[/tex]
We know that the value of [tex]\sin 60^{\circ} = \frac{\sqrt{3} }{2}[/tex]
[tex]\sin y = \frac{\sqrt{3}}{2}[/tex] = [tex]\sin 60^{\circ}[/tex]
On comparing we have;
[tex]y = 60^{\circ} =\frac{\pi}{3}[/tex]
Therefore, the exact value of [tex]\sin^{-1}(\frac{\sqrt{3} }{2})[/tex] is; [tex]\frac{\pi}{3}[/tex]
