Find the Exact Value sin(-210 degrees )

Problem

sin(−210)

Solution

1. Use the odd function property of the sine function, which states that sin(−θ)=−sin(θ)

sin(−210)=−sin(210)

2. Find the reference angle for 210 Since 210 is in the third quadrant, subtract 180 from the angle.

Reference Angle=210−180=30

3. Determine the sign of the sine function in the third quadrant. In the third quadrant, sine is negative.

sin(210)=−sin(30)

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

sin(210)=−1/2

5. Apply the negative sign from the first step to find the final value.

−sin(210)=−(−1/2)=1/2

Final Answer

sin(−210)=1/2

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