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Ch. 1: Preliminaries 1.6 Trigonometric Functions
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Radian Measure
A unit circle is a circle
with a radius of one. x2 + y2 = 1
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Outside of the context of a Cartesian Coordinate system (x-y
plane), negative angles don't generally make sense.
Angle Convention: Use Radians
All angles are measured in radians in this course unless degree is
stated. For example, angle /3 means /3 radians (which is 600)
not /3 degree.
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Ch. 1: Preliminaries 1.6 Trigonometric Functions
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The Six Basic Trigonometric Functions
Defining the trigonometric function of an acute angle in terms
of the sides of a right triangle.
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We can use the following diagram to
decide in which quadrant the sin , cos
and tan arepositive or negative.
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Example
Solution
Then we can get the other trigonometric
functions :
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Periodicity and Graphs of the Trigonometric Functions
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Periods of Trigonometric
Functions
The Symmetries in the graphs in the previous slide reveal thatthe cosine and secant functions are even and the other four
functions are odd:
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Identities
Addition
Formulas
DoubleAngle
Function
HalfAngle
Function
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The low of Cosines
Transformations of Trigonometric graphs
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Example
Solution
How this function appears on the plane.
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Solution
Solution
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Solution
In this function the x is
divided by 2, which
means stretching the
graph horizontally by
factor 2.
Horizontally scaling tell us how the period is changed fromstandard period (2) by factor of 2. Thus the Period for this
function is 4.
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Solution
X is shifted pi/4 to the left,while the total function is
shifted 1 unit to down.
There is no horizontally scaling. Thus the period will stays
standard period (2).
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Solution
Solution
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Solution
Solution
Solve 1 ---to---22, 31---to---36, and 39---to---50.