Find the Exact Value sin(135 degrees )

Problem

sin(135)

Solution

1. Identify the angle in the coordinate plane. The angle 135 is located in the second quadrant (90<135<180.

2. Determine the reference angle. The reference angle θ′ for an angle in the second quadrant is calculated as 180−θ

θ′=180−135=45

3. Apply the sine function properties. In the second quadrant, the sine function is positive. Therefore, sin(135)=sin(45)

4. Evaluate the exact value using the unit circle or special right triangles. The sine of 45 is √(,2)/2

sin(45)=√(,2)/2

Final Answer

sin(135)=√(,2)/2

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