Find the Value Using the Unit Circle tan(45 degrees )

Problem

tan(45)

Solution

1. Identify the coordinates on the unit circle for the given angle 45

2. Recall that for any angle θ on the unit circle, the coordinates are (cos(θ),sin(θ))

3. Determine the values for 45 which are (√(,2)/2,√(,2)/2)

4. Apply the formula for the tangent function, which is defined as the ratio of the sine to the cosine.

tan(θ)=sin(θ)/cos(θ)

5. Substitute the known values into the formula.

tan(45)=√(,2)/2/√(,2)/2

6. Simplify the expression by dividing the identical numerator and denominator.

tan(45)=1

Final Answer

tan(45)=1

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