Find the Value Using the Unit Circle sin(-135)

Problem

sin(−135^∘)

Solution

1. Find a coterminal angle by adding 360^∘ to the negative angle to locate its position on the unit circle.

−135^∘+360^∘=225^∘

2. Identify the quadrant for the angle 225^∘ Since 180^∘<225^∘<270^∘ the angle lies in Quadrant III.

3. Determine the reference angle by subtracting 180^∘ from the angle.

225^∘−180^∘=45^∘

4. Apply the sine value for the reference angle 45^∘ from the unit circle.

sin(45^∘)=√(,2)/2

5. Determine the sign based on the quadrant. In Quadrant III, the sine function (the y-coordinate) is negative.

sin(−135^∘)=−√(,2)/2

Final Answer

sin(−135^∘)=−√(,2)/2

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