Use the unit circle to extend trig functions to all real-number radian measures.
Reduce a radian angle and evaluate exact trig values
Problem
Reduce \(θ~=~13\pi~/6\) to its unique coterminal angle in \([0,~2\pi~)\). Use the diagram to give the exact terminal point and separate sine, cosine, and tangent values.
An angle beyond one revolution becomes familiar after removing complete turns of two pi, which does not change its terminal point or trig values. Once the reduced angle lies in the standard interval, use its special-angle coordinates for cosine and sine. Compute tangent from their quotient and confirm its sign from the quadrant.
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