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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