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

Want more problems? Check here!