WEBVTT

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Here is the problem: Find sin, cos and tan of 2pi/3 on the unit circle.

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Unit circle values for 120° (2pi/3 rad).

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

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Locate the terminal side: in Quadrant II. In Quadrant II sine is positive and cosine is 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 1 over 2, the square root of 3 over 2; tan theta equals negative the square root of 3.

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120° (2pi/3 rad) ends in Quadrant II with a reference angle of 60°. sin theta equals the square root of 3 over 2, cos theta equals negative 1 over 2, tan theta equals negative the square root of 3, csc theta equals 2the square root of 3 over 3, sec theta equals negative 2, cot theta equals negative the square root of 3 over 3.

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