Simplify tan(225)

Problem

tan(225)

Solution

1. Identify the angle's position on the unit circle. The angle 225 is in the third quadrant because 180<225<270

2. Calculate the reference angle. For an angle in the third quadrant, the reference angle (θ_ref) is found by subtracting 180 from the angle.

(θ_ref)=225−180=45

3. Determine the sign of the function. In the third quadrant, the tangent function is positive because both sine and cosine are negative.

tan(225)=tan(45)

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

tan(45)=1

Final Answer

tan(225)=1

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