Find the Exact Value sin(330 degrees )

Problem

sin(330)

Solution

1. Identify the quadrant of the angle 330 Since 270<330<360 the angle lies in the fourth quadrant.

2. Determine the sign of the sine function in the fourth quadrant. In the fourth quadrant, the ycoordinate is negative, so sin(330) must be negative.

3. Calculate the reference angle. The reference angle θ′ for an angle in the fourth quadrant is found by subtracting the angle from 360

θ′=360−330

θ′=30

4. Apply the reference angle property. The value of the trigonometric function of the original angle is equal to the function of the reference angle, adjusted for the quadrant's sign.

sin(330)=−sin(30)

5. Substitute the known exact value for sin(30) which is 1/2

sin(330)=−1/2

Final Answer

sin(330)=−1/2

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