Lesson 4.4

Graphing Trig Functions

Lesson Overview

Graph Trig Parent functions and write down the properties of six parent trig functions such as: Domain, Range, Symmetry, Y-intercept, x-intercept, and at what x value does the function have max and min value.

Use sinusoidal functions to solve problems.

Graphing Sine Function

Properties

Real World Application:

In this example, the acoustician is reading a pattern of sound waves that happens to be in a sine pattern.
The period is a variation of 2π.
The minimum value is -1 an the maximum value is 1.
The values go on forever showing that the domain is (-∞ ,∞ )

SAT Prep Question:

f(x)=2πsin(2πx) - What is the amplitude of the equation?

to find the amplitude of a sin equation you can look at the number ahead of the sin.
in this case, we can look at the 2π in front of the sin function
the amplitude of this function is 2π.

Graphing Cosine Function

Properties

Real World Application:

In this application is showing how a scientist is studying the pattern of weather in weeks, after the spring equinox.
They have messed with the original formula, making small translations in the graph.
But overall, you can tell the period of which the cosine function repeats.

SAT Prep Question:

f(x)=4cos(πx/5)

to find the amplitude of a cos equation you can look at the number ahead of the cos.
in this case, we can look at the 4 in front of the cos function
the amplitude of this function is 4.

Use Sinusoidal Functions to Solve Problems

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