Question

Find all solutions to the equation. (1 point) sin x = square root of three divided by two.

Answer 1

$sin x = \frac{\sqrt{3}}{2}$

x = 60° = pi/3 radians

pi/3 is one solution

then

pi - pi/3 = 2 pi/3 is another one

pi/3 + 2.k.pi

2.pi/3 + 2.k.pi

k e Z

Are the solutions

Answer 2

Answer:

x=pi/3 + 2pi*k

x=2pi/3+2pi*k

Step-by-step explanation:

sin(x)=sqrt(3)/2

This happens twice in the first rotation on our unit circle.

It happens in the first quadrant and in the second quadrant. Third and fourth quadrants are negative for sine.

So we are looking for when the y-coordinate on the unit circle is sqrt(3)/2.

This is at pi/3 and 2pi/3.

So we can get all the solutions by adding +2pi*k to both of those.  This gives us a full rotation about the circle any number of k times. k is an integer.

So the solutions are

x=pi/3 + 2pi*k

x=2pi/3+2pi*k