Evaluate sin(-135 degrees )

Problem

sin(−135)

Solution

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

sin(−135)=−sin(135)

2. Find the reference angle for 135 by subtracting it from 180 since it lies in the second quadrant.

Reference Angle=180−135=45

3. Determine the sign of the sine function in the second quadrant. Since sine is positive in the second quadrant, sin(135)=sin(45)

−sin(135)=−sin(45)

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

−sin(45)=−√(,2)/2

Final Answer

sin(−135)=−√(,2)/2

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