Find the Value Using the Unit Circle sin(135)

Problem

sin(135^∘)

Solution

1. Identify the position of 135^∘ on the unit circle. Since 90^∘<135^∘<180^∘ the angle lies in Quadrant II.

2. Calculate the reference angle θ^′ In Quadrant II, the reference angle is found by subtracting the angle from 180^∘

θ^′=180^∘−135^∘

θ^′=45^∘

3. Determine the sign of the sine function. In Quadrant II, the ycoordinates are positive, so sin(135^∘) is positive.

4. Apply the known value for the reference angle. On the unit circle, the sine of 45^∘ is √(,2)/2

sin(135^∘)=sin(45^∘)

sin(135^∘)=√(,2)/2

Final Answer

sin(135^∘)=√(,2)/2

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