Find the Exact Value tan(-225 degrees )

Problem

tan(−225)

Solution

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

tan(−225)=−tan(225)

2. Find the reference angle for 225 Since 225 is in the third quadrant, subtract 180 from the angle.

Reference Angle=225−180=45

3. Determine the sign of the tangent function in the third quadrant. Tangent is positive in the third quadrant.

tan(225)=tan(45)

4. Evaluate the tangent of the reference angle using known trigonometric values.

tan(45)=1

5. Substitute the value back into the expression from step 1.

−tan(225)=−(1)=−1

Final Answer

tan(−225)=−1

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