Question

find all real numbers that satisfy the equation: sinx= -\sqrt3/ 2

Answer 1

review your "standard angles."

sin π/3 = √3/2

sine is negative in QIII and QIV. That means that

sin(π+π/3) = sin(2π-π/3) = -√3/2

Now you can add any multiple of 2π to those values, and you get all real numbers as required.

If you draw a circle of radius r around the origin, and mark the point (x,y) on the circle, at an angle θ, measured from the positive x-axis,

sin θ = y/r

So, since r is always positive, you need y < 0 to have a negative sine.