Complete the general solution to y = arcsin - ( √(3) )/(2)y=___+-2πkSelect all that apply.π/3(2π)/3(4π)/3(5π)/3

Question

Complete the general solution to
`y = arcsin - ( √(3) )/(2)`y=___+-2πkSelect all that apply.π/3(2π)/3(4π)/3(5π)/3

Answer 1

To find the general solution to y we need take the sine function in both sides of the equation given:

`\begin{gathered} \sin y=\sin (\sin ^(-1)-\frac{\sqrt[]{3}}{2}) \\ \sin y=-\frac{\sqrt[]{3}}{2} \end{gathered}`

Now, we have to find the value of y for which the sine function is equal to the right side. From the properties of the sine function and its definition we conclude that y has to be:

`y=(5\pi)/(3)`

Therefore the general solution is:

`y=(5\pi)/(3)\pm2\pi k`