Select all that apply. solve for x, 0 < x < 2 pie. 2 sin x - sqrt 3 = 0 < is actually less than or equal to sign. sqrt means square root. answer choices (select all that apply) pie/3 2pie/3 4pie/3 5pie/3

A and B

pi/3 and 2pi/3

Work Shown:

2*sin(x) - sqrt(3) = 0

2sin(x) = sqrt(3)

sin(x) = sqrt(3)/2

Using the unit circle, we see that sin(theta) is equal to sqrt(3)/2 when theta is theta = pi/3 in quadrant I, and when theta = 2pi/3 in quadrant II.

So sin(pi/3) = sqrt(3)/2 and sin(2pi/3) = sqrt(3)/2

You can check these answers by replacing x with the value in question and seeing if you get zero. Make sure your calculator is in radian mode

Plug in x = pi/3

2*sin(x) - sqrt(3) = 0

2*sin(pi/3) - sqrt(3) = 0

0 = 0 this is a true equation, x = pi/3 is confirmed as a solution

Plug in x = 2pi/3

2*sin(x) - sqrt(3) = 0

2*sin(2pi/3) - sqrt(3) = 0

0 = 0 true equation, x = 2pi/3 is confirmed as a solution

Plug in x = 4pi/3

2*sin(x) - sqrt(3) = 0

2*sin(4pi/3) - sqrt(3) = 0

-3.4641016 = 0 false equation, x = 4pi/3 is a nonsolution

Plug in x = 5pi/3

2*sin(x) - sqrt(3) = 0

2*sin(5pi/3) - sqrt(3) = 0

-3.4641016 = 0 false equation, x = 5pi/3 is a nonsolution