Find the Exact Value sin(135)

Problem

sin(135)

Solution

1. Identify the angle in the coordinate plane. The angle 135 is located in the second quadrant (Quadrant II).

2. Determine the reference angle. For an angle θ in Quadrant II, the reference angle θ′ is calculated as 180−θ

θ′=180−135=45

3. Determine the sign of the function. In Quadrant II, the sine function is positive.

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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