Find the Exact Value tan(-135 degrees )

Problem

tan(−135)

Solution

1. Use the odd function property of the tangent function, which states that tan(−θ)=−tan(θ)

tan(−135)=−tan(135)

2. Find the reference angle for 135 Since 135 is in the second quadrant, the reference angle is 180−135

(θ_ref)=45

3. Determine the sign of the tangent function in the second quadrant. In Quadrant II, sine is positive and cosine is negative, so tangent is negative.

tan(135)=−tan(45)

4. Substitute the known value for tan(45) which is 1

tan(135)=−1

5. Apply the initial negative sign from the odd function property to find the final result.

−tan(135)=−(−1)

1

Final Answer

tan(−135)=1

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