Radians

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Radians
SIN-L2 Objectives To understand radian angle
measurement.
Learning Outcome B-4
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Most graphing software uses radians rather than
degrees to measure angles. For this reason, you
must know how to use radian measures to draw or
analyze graphs of sinusoidal functions. In this
lesson, we introduce radians and look at how
degrees and radians compare.
Intro Radian Measure
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One radian (written as 1r) is the angle at the
centre of a circle when a radius of the circle is
rotated through an arc that is the same length as
the radius. NoteRadian measures are
'natural' measurements because the angle of one
radian is based on radius and arc lengths. Degree
measures are 'artificial' measurements because
someone decided that a circle should be
subdivided into 360 parts called degrees. The
value of 360 was probably used because there are
approximately 360 days in a year.
Intro One Radian
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In the diagram below, the arc length is the same
as the radius, and the central angle is one
radian.
If we draw similar arcs until we have a complete
semicircle, we now have approximately 3.14 arcs,
and a central angle of approximately 3.14r in a
semicircle. We will always get this result,
regardless of the size of the circle. This
implies a technique of counting radian measure
using increments of 3.14, or p. There are p
radians in a semicircle, 2p radians in a full
circle.
Theory Semicircle Angle Measure
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On the previous page, you saw that180 p
rThe table below shows some commonly used
measurements as degrees and radians. It is useful
to be familiar with the radian measurements of
some commonly used angles.
Theory Radian / Degree Equivalent Measures
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To convert from one system to the other, we the
same conversion ratio techniques that weve used
since 20S Applied (metric gt imperial, 2D3D scale
factors, etc.) 180 p r Rewrite 35 as a
radian measure. Rewrite as degrees.
Theory Conversion Ratios
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Convert to radians
Convert to degrees
Practice Conversion Ratios
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In Lesson 1, you drew a sinusoidal graph from
data (relating the vertical segment length and
the angle of rotation). The graph was similar to
the one shown below. We will now use
graphing software to draw sinusoidal graphs. The
software used in this course is Graphmatica.
Graphmatica
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Graphmatica
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Graphmatica