Find the Exact Value sin(330)

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 (θ_r*e*ƒ) For an angle in the fourth quadrant, the reference angle is found by subtracting the angle from 360

(θ_r*e*ƒ)=360−330

(θ_r*e*ƒ)=30

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

sin(330)=−sin(30)

5. Substitute the known exact value for sin(30)

sin(30)=1/2

sin(330)=−1/2

Final Answer

sin(330)=−1/2

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