Problem

Use the unit-circle diagram to reduce \(θ~=~-\pi~/6\) to \([0,~2\pi~)\), then give its terminal point and exact sine, cosine, and tangent values.

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What this problem is really about

Reduce a directed angle by whole turns before reading its unit-circle values; coterminal angles share the same endpoint. Use the reduced quadrant to attach signs to the familiar reference-angle coordinates, then read cosine first and sine second. Form tangent last, checking whether its cosine denominator is zero before simplifying.

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The least nonnegative coterminal angle is 11pi/6; the terminal point is (sqrt(3)/2, -1/2); sin(theta) = -1/2, cos(theta) = sqrt(3)/2, and tan(theta) = -sqrt(3).

The least nonnegative coterminal angle is 11pi/6; the terminal point is (sqrt(3)/2, -1/2); sin(theta) = -1/2, cos(theta) = sqrt(3)/2, and tan(theta) = -sqrt(3)/3.

The least nonnegative coterminal angle is -pi/6; the terminal point is (sqrt(3)/2, -1/2); sin(theta) = -1/2, cos(theta) = sqrt(3)/2, and tan(theta) = -sqrt(3)/3.

The least nonnegative coterminal angle is 11pi/6; the terminal point is (sqrt(3)/2, -1/2); sin(theta) = sqrt(3)/2, cos(theta) = -1/2, and tan(theta) = -sqrt(3).

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Use the unit-circle diagram to reduce \(θ~=~-\pi~/6\) to \([0,~2\pi~)\), then give its terminal point and exact sine, cosine, and tangent values.

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