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Here is the problem: Find sin, cos and tan of 210° on the unit circle.

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Unit circle values for 210°.

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Convert degrees to radians (multiply by pi/180).

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Locate the terminal side: in Quadrant III. In Quadrant III sine and cosine are both negative (“All Students Take Calculus”).

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Reference angle (acute angle to the x-axis).

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Read the exact coordinates from the reference angle and apply the quadrant signs.

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Tangent equals sine divided by cosine.

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Reciprocal functions.

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So the answer is (cos theta, sin theta) equals (negative the square root of 3 over 2, negative 1 over 2); tan theta equals the square root of 3 over 3.

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210° (7pi/6 rad) ends in Quadrant III with a reference angle of 30°. sin theta equals negative 1 over 2, cos theta equals negative the square root of 3 over 2, tan theta equals the square root of 3 over 3, csc theta equals negative 2, sec theta equals negative 2the square root of 3 over 3, cot theta equals the square root of 3.

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cos squaredtheta plus sin squaredtheta equals 1 (must equal 1).