Multiple choice

The smallest value of an angle whose sine is $-\frac{\sqrt{3}}{2}$ is

  1. $30^0$
  2. $60^0$
  3. $120^0$
  4. $240^0$
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D Correct answer
Explanation

Sine is negative in the third and fourth quadrants. sin(x) = -sqrt(3)/2 corresponds to reference angle 60 degrees. In the third quadrant, the angle is 180 + 60 = 240 degrees.

AI explanation

The sine function is negative in the third and fourth quadrants, with a reference angle of 60 degrees because sin(60) = sqrt(3)/2. To find the smallest positive angle in the third quadrant, we calculate 180 + 60 = 240 degrees. Therefore, the smallest value of the angle is 240 degrees.

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