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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