Find the Exact Value tan(225 degrees )

Problem

tan(225)

Solution

1. Identify the quadrant of the angle. Since 180<225<270 the angle 225 lies in the third quadrant (Quadrant III).

2. Determine the reference angle. In the third quadrant, the reference angle (θ_ref) is calculated as θ−180

(θ_ref)=225−180=45

3. Determine the sign of the function. In Quadrant III, the tangent function is positive.

tan(225)=tan(45)

4. Evaluate the trigonometric function using the known value for the reference angle.

tan(45)=1

Final Answer

tan(225)=1

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