Find the Exact Value sin(570)

Problem

sin(570)

Solution

1. Find the coterminal angle by subtracting 360 from 570 to bring the angle within the standard range of 0 to 360

570−360=210

2. Determine the quadrant for 210 Since 180<210<270 the angle lies in Quadrant III.

3. Find the reference angle for an angle in Quadrant III by subtracting 180 from the angle.

(θ_ref)=210−180=30

4. Determine the sign of the sine function in Quadrant III. In Quadrant III, the sine value is negative.

sin(210)=−sin(30)

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

sin(30)=1/2

6. Apply the sign to find the final exact value.

sin(570)=−1/2

Final Answer

sin(570)=−1/2

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