Find the Exact Value tan(pi/4)

Problem

tan(π/4)

Solution

1. Identify the angle in the unit circle. The angle π/4 radians is equivalent to 45

2. Recall the coordinates on the unit circle for π/4 At this angle, the xcoordinate and ycoordinate are equal.

3. Apply the formula for the tangent function, which is defined as the ratio of the ycoordinate to the xcoordinate.

tan(θ)=y/x

4. Substitute the known values for π/4 where x=√(,2)/2 and y=√(,2)/2

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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