WEBVTT

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Here is the problem: Find sin, cos and tan of 5pi/4 on the unit circle.

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Unit circle values for 225° (5pi/4 rad).

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

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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 2 over 2, negative the square root of 2 over 2; tan theta equals 1.

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225° (5pi/4 rad) ends in Quadrant III with a reference angle of 45°. sin theta equals negative the square root of 2 over 2, cos theta equals negative the square root of 2 over 2, tan theta equals 1, csc theta equals negative the square root of 2, sec theta equals negative the square root of 2, cot theta equals 1.

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