Evaluate tan(135 degrees )

Problem

tan(135)

Solution

1. Identify the angle in the coordinate plane. The angle 135 is located in the second quadrant.

2. Determine the reference angle. Since the angle is in the second quadrant, the reference angle is 180−135=45

3. Apply the trigonometric identity for the tangent of an angle in the second quadrant. In the second quadrant, the tangent function is negative.

4. Evaluate the tangent of the reference angle. We know that tan(45)=1

5. Combine the sign and the value to find the final result.

Final Answer

tan(135)=−1

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