Question

Solve the given equation over the interval [0, 2pi)
2sin x - sqrt(3) = 0

x = pi/3 and x = 2pi/3
x == 7pi/6 and x = 11pi/6
x = pi/6 and x = 5pi/6
x = 4pi/3 and x = 5pi/3

Answer 1

isolate sin(x)

2sin(x)=sqrt(3)

sin(x)=sqrt(3)/2

So, we know that the sin(x) is the sqrt(3)/2 on the unit circle. In other words, if were to draw a circle that has a radius of one foot(a unit circle, or in this case a foot circle), where on the circle would the point be sqrt(3)/2 feet over the x axis? I know of only two points; when x is pi/3, and when x is 2pi/3. The other two places are negative, so those won't work, unless the question said that the sin(x) is always positive.