Simplify tan(135)

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

3. Calculate the reference angle value:

180^∘−135^∘=45^∘

4. Determine the sign of the tangent function in the second quadrant. In the second quadrant, the tangent of an angle is negative.

5. Apply the trigonometric identity for the reference angle:

tan(135^∘)=−tan(45^∘)

6. Substitute the known value for tan(45^∘) which is 1

−1

Final Answer

tan(135^∘)=−1

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