WEBVTT

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Here is the problem: Find sin, cos and tan of 30° on the unit circle.

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Unit circle values for 30°.

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

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Locate the terminal side: in Quadrant I. In Quadrant I sine and cosine are both 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 (the square root of 3 over 2, 1 over 2); tan theta equals the square root of 3 over 3.

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