Evaluate sin(210 degrees )

Problem

sin(210)

Solution

1. Identify the reference angle by determining how far 210 is from the horizontal axis (180.

Reference Angle=210−180=30

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

3. Determine the sign of the sine function in Quadrant III. In this quadrant, the ycoordinates are negative, so sin(θ) is negative.

sin(210)=−sin(30)

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

sin(30)=1/2

5. Apply the negative sign to find the final value.

sin(210)=−1/2

Final Answer

sin(210)=−1/2

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