Select all of the following that represent the exact solutions of sin(x)=sqrt(3)/2

Step: take the inverse sine of both side of the equation

x=arcsin (√3/2)

The exact value of arcsin (√3/2) is π/3

Step 2: the sine function is positive in the 1st and 2nd quadrants. Therefore to find the solution in the second quadrant we need to subtract the reference angle from π.

x= π - π/3

We need to simply and comes out as x= 2 π/3

Answer: x= π/3 and x= 2π/3

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abidemiokin abidemiokin · Answer 2 · 2021-10-29T18:33:47+02:00

The values of x that represent the exact solutions of the equation are [tex]\frac{\pi}{3} \ and \ \frac{2\pi}{3}[/tex]

Given the trigonometry expression [tex]sin(x)=\frac{\sqrt{3}}{2}[/tex]

We are to get all the positive values of "x"

Take the arcsin of both sides

[tex]sin^{-1}sin(x)=sin^{-1}\frac{\sqrt{3}}{2}\\x =sin^{-1}\frac{\sqrt{3}}{2}\\x=60^0\\x=\frac{\pi}{3}[/tex]

Since [tex]sin\theta[/tex] is positive in the second quadrant, another exact solution to the system of equation is expressed as [tex]\pi - \frac{\pi}{3}=\frac{2\pi}{3}[/tex]

This shows that the values of x that represent the exact solutions of the equation are [tex]\frac{\pi}{3} \ and \ \frac{2\pi}{3}[/tex]

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