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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