Find the Value Using the Unit Circle tan(pi/4)

Problem

tan(π/4)

Solution

1. Identify the angle on the unit circle. The angle π/4 radians is located in the first quadrant.

2. Determine the coordinates (x,y) at this angle. On the unit circle, the point corresponding to π/4 is (√(,2)/2,√(,2)/2)

3. Apply the formula for the tangent function. The tangent of an angle is defined as the ratio of the y-coordinate to the x-coordinate.

tan(θ)=y/x

4. Substitute the values into the formula.

tan(π/4)=√(,2)/2/√(,2)/2

5. Simplify the fraction. Since the numerator and denominator are identical and non-zero, the result is 1.

Final Answer

tan(π/4)=1

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