Find the Exact Value 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 135 is in the second quadrant, the reference angle is calculated as 180−135=45

3. Apply the tangent property for 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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