AyeletX142154 AyeletX142154
  • 03-11-2022
  • Mathematics
contestada

Complete the general solution to [tex]y = arcsin - \frac{ \sqrt{3} }{2} [/tex]y=___+-2πkSelect all that apply.π/3(2π)/3(4π)/3(5π)/3

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CannonE701677 CannonE701677
  • 03-11-2022

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

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

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:

[tex]y=\frac{5\pi}{3}[/tex]

Therefore the general solution is:

[tex]y=\frac{5\pi}{3}\pm2\pi k[/tex]

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