Simplify sin(135)

Problem

sin(135)

Solution

1. Identify the angle in the unit circle. The angle 135 is located in the second quadrant.

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

3. Calculate the reference angle value.

θ′=180−135=45

4. Determine the sign of the sine function. In the second quadrant, the sine function is positive.

5. Evaluate the sine of the reference angle using known trigonometric values.

sin(45)=√(,2)/2

Final Answer

sin(135)=√(,2)/2

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