LESSON 4.4

Graphing Trigonometric Functions

Lesson Overview:

graphing cos, sin and identifying Parent function, domain, range, symmetry, x-intercept, y-intercept, and max & min.

a. Sine Function

b. Cosine Function

Part A: Graphing Sin Functions

The Parent sine function is f (t) = sin(t).

This function has an amplitude of 1 because the graph goes

one unit up and one unit down from the mid-line of the graph.

This function has a period of 2π because the sine wave

repeats every 2π units.

Part B: Graphing Cotangent Functions

y=cos(x)

Graphing Trig Functions on the SAT

First, let's use the given information to determine the function's amplitude, mid-line, and period.

Then, we should determine whether to use a sine or a cosine function, based on the point where x=0, equals, 0.

Finally, we should determine the parameters of the function's formula by considering all the above.

The mid-line intersection is at y=3 so this is the mid-line.

The maximum point is 4 units above the mid-line, so the amplitude is 4.

The mid-line intersection is 3 units to the right of the maximum point, so the period is 12.

Since the graph has an extremum point at x=0, we should use the cosine function and not the sine function.

a=4, d=3, b= π/6

answer: y= 4cos (π/6* x) +3

Graphing Trig Functions in the Real World

Conclusion:

In order to graph trigonometric functions you first must identify the amplitude (how far up and down the graph covers) and the period of the function which is how many units a single wave is.

g(t) = 3sin(t)

The second graph is three times as tall as our parent function. The amplitude has changed from 1 to 3 .Whatever number A is multiplied on the trig function gives you the amplitude (that is, the "tallness" or "shortness" of the graph); in this case, that amplitude number was 3.

h(t) = sin(2t)

This third graph is squished in from the sides compared to the first graph and the sine wave is appearing twice as much. This relationship is always true: Whatever value B is multiplied on the variable (inside the trig function), you use this value to find the period.

j(t) = sin(t – π/3)

The blue graph is shifted over π/3 units from the regular graph. The graph is shifted to the right or left by that number of units This right- or left-shifting is called "phase shift".