Find the Exact Value sin(690)

Problem

sin(690)

Solution

1. Find the coterminal angle by subtracting multiples of 360 until the angle is between 0 and 360

690−360=330

2. Determine the quadrant for the angle 330 Since 270<330<360 the angle lies in Quadrant IV.

3. Find the reference angle for an angle in Quadrant IV by subtracting the angle from 360

360−330=30

4. Apply the sign rule for the sine function. In Quadrant IV, the sine of an angle is negative.

sin(330)=−sin(30)

5. Evaluate the sine of the reference angle using known trigonometric values.

sin(30)=1/2

6. Combine the results to find the final value.

sin(690)=−1/2

Final Answer

sin(690)=−1/2

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