1.6 Trigonometric Functions

7/27/2019 1.6 Trigonometric Functions

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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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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.

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1.6 Trigonometric Functions