WEBVTT

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Here is the problem: Find sin, cos and tan of negative 60° on the unit circle.

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Unit circle values for negative 60°.

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

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Find the coterminal angle between 0° and 360°. Add or subtract full turns of 360° (2pi); trigonometric values repeat every full turn.

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

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