Find the Exact Value tan(-(17pi)/6)

Problem

tan(−(17*π)/6)

Solution

1. Identify the periodicity of the tangent function. Since tan(θ) has a period of π we can add multiples of π to the angle without changing the value.

2. Add multiples of π to find a coterminal angle within the interval [0,π)

−(17*π)/6+3*π=−(17*π)/6+(18*π)/6

π/6

3. Evaluate the tangent of the coterminal angle using the unit circle or special triangles.

tan(π/6)=sin(π/6)/cos(π/6)

4. Substitute the known values sin(π/6)=1/2 and cos(π/6)=√(,3)/2

1/2/√(,3)/2=1/√(,3)

5. Rationalize the denominator by multiplying the numerator and denominator by √(,3)

1/√(,3)⋅√(,3)/√(,3)=√(,3)/3

Final Answer

tan(−(17*π)/6)=√(,3)/3

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