Question

Complete the general solution to $y = arcsin - \frac{ \sqrt{3} }{2}$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:

$y=\frac{5\pi}{3}$

Therefore the general solution is:

$y=\frac{5\pi}{3}\pm2\pi k$