Evaluate tan(45 degrees )

Problem

tan(45)

Solution

1. Identify the angle in the context of the unit circle or a special right triangle.

2. Recall that for an angle of 45 the coordinates on the unit circle are (√(,2)/2,√(,2)/2)

3. Apply the definition of the tangent function, which is the ratio of the sine to the cosine of the angle.

tan(θ)=sin(θ)/cos(θ)

4. Substitute the known values for sin(45) and cos(45) into the formula.

tan(45)=√(,2)/2/√(,2)/2

5. Simplify the fraction by noting that any non-zero number divided by itself equals 1

Final Answer

tan(45)=1

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