using the graph of ysinx list all values on the interval 5pi

using the graph of y=sinx, list all values on the interval [-5pi/3, 10pi/3] that satisfy the ordered pair (x, -root3/2)

Solution

y = sin x

that satisfy the ordered pair ( x . - sqrt 3/2 )

plugging y = - sqrt 3/ 2

- sqrt 3/2 = sin x

x = 4pi/3 + 2pin , x = 5pi/3 + 2pin

in the inerval [-5pi/3, 10pi/3]

solutions are

x = -pi/3 , 5pi/3 , -2pi/3 , 10pi/3 , 4pi/3