Find the Exact Value tan((5pi)/2)

Problem

tan((5*π)/2)

Solution

1. Identify the angle in terms of its position on the unit circle.

2. Simplify the angle by subtracting multiples of 2*π to find the coterminal angle within the interval [0,2*π)

(5*π)/2−2*π=(5*π)/2−(4*π)/2

(5*π)/2−(4*π)/2=π/2

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

tan(π/2)=sin(π/2)/cos(π/2)

4. Substitute the known values for the sine and cosine of π/2 from the unit circle.

sin(π/2)=1

cos(π/2)=0

5. Evaluate the resulting fraction. Since the denominator is zero, the expression is undefined.

1/0=Undefined

Final Answer

tan((5*π)/2)=Undefined

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