Find the Exact Value tan((15pi)/6)

Problem

tan((15*π)/6)

Solution

1. Simplify the fraction inside the tangent function by dividing the numerator and denominator by their greatest common divisor, 3.

(15*π)/6=(5*π)/2

2. Find the coterminal angle by subtracting multiples of 2*π until the angle is 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. Evaluate the tangent function at the simplified angle. Recall that tan(θ)=sin(θ)/cos(θ)

tan(π/2)=sin(π/2)/cos(π/2)

4. Identify the values of sine and cosine at π/2

sin(π/2)=1

cos(π/2)=0

5. Determine the result of the division. Since the denominator is zero, the value is undefined.

1/0=Undefined

Final Answer

tan((15*π)/6)=Undefined

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