Respuesta :

altavistard
Think of this as "the angle whose sine is sqrt(3) over 2.  That would be 60 degrees, or pi/3 radians.  Check this by finding sin 60 degrees; the result will be sqrt(3) / 2.

Answer:

[tex]\frac{\pi }{3}[/tex]

Step-by-step explanation:

[tex]sin^{-1}(\frac{\sqrt{3} }{2})[/tex]

In, 30-60-90 degree triangle ,

the sides are in the ratio [tex]1: \sqrt{3} :2[/tex]

[tex]sin(60)= \frac{opposite}{hypotenuse}[/tex]

for 60 degree, opposite side = square root (3)

hypotenuse = 2

So [tex]sin(60)= \frac{\sqrt{3}}{2}[/tex]

when we move sin to the other side then it becomes sin^-1

[tex]60= sin^{-1}\frac{\sqrt{3}}{2}[/tex]

angle 60 degree is [tex]\frac{\pi }{3}[/tex]

[tex]sin^{-1}(\frac{\sqrt{3} }{2})=\frac{\pi }{3}[/tex]

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