Geometry: An Interactive Journey to Mastery

Lesson 16: “Circle-ometry”—On Circular Motion

“Circle-ometry”—On Circular Motion

Lesson 16

Topic

x The sine and cosine of angles computed via points on a circle.

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x FRVLQHRIDQDQJOHͼ௘LQFLUFOHRPHWU\௘ͽ: A point moves in a counterclockwise direction along a circle

of radius 1. If the angle of elevation of the point above the positive horizontal axis is x, then the length

of the horizontal displacement, left or right, of the point

is denoted cos x and is called the cosine of the angle.

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x VLQHRIDQDQJOHͼ௘LQFLUFOHRPHWU\௘ͽ: A point moves in

a counterclockwise direction along a circle of radius 1.

If the angle of elevation of the point above the positive

horizontal axis is x, then the height of the point above the

axis is denoted sin x and is called the sine of the angle.

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Formulas

x sin xx 360° sin.

x cos xx 360° cos.

x sin  xxsin.

x cos  xxcos.

x cos xx^22  sin 1.

Summary

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circle is indeed the natural and appropriate introduction to the subject. This is a preliminary lesson that sets the

stage for trigonometry. In it, we introduce the basic concepts of the sine and cosine of an angle.

x

(^1) sin ͼxͽ
cos ͼxͽ
Figure 16.1