Question

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

Answer 1

Answer: A and B

pi/3 and 2pi/3

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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

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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