Find the Exact Value sin(-225)

Problem

sin(−225)

Solution

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

sin(−225)=−sin(225)

2. Find the reference angle for 225 Since 225 is in the third quadrant, subtract 180 from the angle.

Reference Angle=225−180=45

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

sin(225)=−sin(45)

4. Substitute the known value for sin(45) which is √(,2)/2

sin(225)=−√(,2)/2

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

−sin(225)=−(−√(,2)/2)

sin(−225)=√(,2)/2

Final Answer

sin(−225)=√(,2)/2

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