Evaluate 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 θ in the third quadrant, the reference angle θ′ is found using θ′=θ−180

θ′=225−180=45

3. Determine the sign of the tangent function. In the third quadrant, both sine and cosine are negative, which means the tangent function (sin(θ)/cos(θ) is positive.

tan(225)=tan(45)

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

tan(45)=1

Final Answer

tan(225)=1

Want more problems? Check here!