Find the Value Using the Unit Circle tan(12/5)

Problem

tan((12*π)/5)

Solution

1. Identify the angle and determine if it is within the standard interval of [0,2*π)

2. Find the coterminal angle by subtracting 2*π from the given angle.

(12*π)/5−2*π=(12*π)/5−(10*π)/5

(12*π)/5−(10*π)/5=(2*π)/5

3. Recognize that (2*π)/5 is equivalent to 72 Since this is not a standard unit circle angle (like 30 45 or 60, the value is typically expressed using the tangent function of the coterminal angle.

4. Apply the periodicity of the tangent function, which states tan(θ+n*π)=tan(θ)

tan((12*π)/5)=tan((2*π)/5+2*π)

tan((2*π)/5+2*π)=tan((2*π)/5)

5. Calculate the numerical value if required, or leave it in exact trigonometric form.

tan((2*π)/5)=√(,5+2√(,5))

Final Answer

tan((12*π)/5)=√(,5+2√(,5))

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