CIRCULAR MEASUREMENTS
INTRODUCTION
Trigonometry is the branch of mathematics concerned with measurement of the parts, sides,
and angles of a triangle. Plane trigonometry, which is the subject of this chapter, is restricted
to triangles lying in a plane. Trigonometry is based on certain ratios, called trigonometric
functions, with the early applications of the trigonometric functions being in surveying,
navigation, and engineering. These functions also play an important role in the study of all
sorts of vibratory phenomena – sound, light, electricity, etc. Consequently, a considerable
portion of the subject matter is concerned with a study of the properties of and relations among
the trigonometric functions.
LEARNING OUTCOMES
On completion of this chapter, you will be able to:
Define (explain) radian measure and perform calculations pertaining to circular
measurements.
Demonstrate basic understanding of trigonometric functions.
Solve trigonometric equations.
Sketch graphs of the sine function and demonstrate understanding of simple harmonic
motion.
COMPILED BY T. PAEPAE
, 3.1 CIRCULAR MEASUREMENTS
Why it is important to understand: Circular Measurements
‘A circle is one of the fundamental shapes of geometry; it consists of all the points that are
equidistant from a central point. Knowledge of calculations involving circles is needed with
crank mechanisms, with determinations of latitude and longitude, with pendulums, and even
in the design of paper clips. The floodlit area at a football ground, the area an automatic garden
sprayer sprays and the angle of lap of a belt drive all rely on calculations involving the arc of
a circle. The ability to handle calculations involving circles and its properties is clearly essential
in several branches of engineering design.’ Bird, J., 2017. Higher engineering mathematics.
Routledge.
SPECIFIC OUTCOMES
On completion of this study unit, you will be able to:
Define a radian.
Convert angular measurements in degrees to angular measurements in radians and
vice versa.
State some properties of a circle – including radius, circumference, diameter, sector,
chord, segment and arc.
Perform calculations with circle sections, such as segments, sectors, arc lengths, radii,
chords, and angles.
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INTRODUCTION
Trigonometry is the branch of mathematics concerned with measurement of the parts, sides,
and angles of a triangle. Plane trigonometry, which is the subject of this chapter, is restricted
to triangles lying in a plane. Trigonometry is based on certain ratios, called trigonometric
functions, with the early applications of the trigonometric functions being in surveying,
navigation, and engineering. These functions also play an important role in the study of all
sorts of vibratory phenomena – sound, light, electricity, etc. Consequently, a considerable
portion of the subject matter is concerned with a study of the properties of and relations among
the trigonometric functions.
LEARNING OUTCOMES
On completion of this chapter, you will be able to:
Define (explain) radian measure and perform calculations pertaining to circular
measurements.
Demonstrate basic understanding of trigonometric functions.
Solve trigonometric equations.
Sketch graphs of the sine function and demonstrate understanding of simple harmonic
motion.
COMPILED BY T. PAEPAE
, 3.1 CIRCULAR MEASUREMENTS
Why it is important to understand: Circular Measurements
‘A circle is one of the fundamental shapes of geometry; it consists of all the points that are
equidistant from a central point. Knowledge of calculations involving circles is needed with
crank mechanisms, with determinations of latitude and longitude, with pendulums, and even
in the design of paper clips. The floodlit area at a football ground, the area an automatic garden
sprayer sprays and the angle of lap of a belt drive all rely on calculations involving the arc of
a circle. The ability to handle calculations involving circles and its properties is clearly essential
in several branches of engineering design.’ Bird, J., 2017. Higher engineering mathematics.
Routledge.
SPECIFIC OUTCOMES
On completion of this study unit, you will be able to:
Define a radian.
Convert angular measurements in degrees to angular measurements in radians and
vice versa.
State some properties of a circle – including radius, circumference, diameter, sector,
chord, segment and arc.
Perform calculations with circle sections, such as segments, sectors, arc lengths, radii,
chords, and angles.
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