Graphing Primary and Reciprocal Trig Functions

MHF4UIMonday November 12th, 2012

Defining a Trig Function

We have spent the last classes solving for angles with the help of the primary and reciprocal Trig Ratios.

Each trig ratio can be expressed as a function of each angle

Let’s start by examining the Trig Ratio Sine as a function of , which can be written as:

or

or

For each inputted angle , the sine function will output the corresponding sine ratio:

𝑦=sin 𝑥

sin 0=0

This is a graph of the sine function

𝑦=sin 𝑥

Characteristics of

Maximum value: 1Minimum value: -1

Y-intercept: X-intercepts:

Amplitude = 1Period =

Amplitude and Period

Amplitude is half the distance between the minimum and maximum values of the

range of a periodic function

A period is how often the function will complete 1 full cycle or oscillation

Amplitude = 1Period =

𝑎=1

𝑃=2𝜋

Graph of

Graphing Sine and Cosine Functions

When we graph the sine and cosine functions we can use the angle to help determine the shape of the graph.At each increment of we will have a maximum, a minimum or an x-intercept.

For the cosine function:Maximums occur at Minimums occur at X-intercepts occur at

Characteristics of

Maximum value: 1Minimum value: -1

Y-intercept: X-intercepts:

Amplitude = 1Period =

The Reciprocal Function Cosecant

We know we can plot the points of the reciprocal trig function cosecant by using the sine function.

Characteristics of

Maximum value: Minimum value:

Y-intercept: X-intercept:

Vertical Asymptotes at:

Amplitude: Period =

The Reciprocal Function Secant

We know we can plot the points of the reciprocal trig function cosecant by using the cosine function.

Characteristics of

Maximum value: Minimum value:

Y-intercept: X-intercept:

Vertical Asymptotes at:

Amplitude: Period =

Graphing Secant and Cosecant Functions

When we graph the Secant and Cosecant functions we can use

increments of to draw our graph.

Each increment of will either be a Minimum or a vertical asymptote.

For Sine and Cosine functions:x-intercepts vertical asymptotes

on reciprocal graph

Max/Min Values will be the same on the reciprocal graph

The Trig Function Tangent

Characteristics of

Maximum value: Minimum value:

Y-intercept: X-intercepts:

Vertical Asymptotes at:

Amplitude: Period =

The Reciprocal Function Cotangent

We can plot the points of the reciprocal trig function cotangent by using the tangent function.

Characteristics of Maximum value: Minimum value:

Y-intercept: X-intercepts:

Vertical Asymptotes at:

Amplitude: Period =

Homework Questions:

Complete the Primary and Reciprocal Trig Function Summary Handout

Using only your calculator, graph each of the Primary and Reciprocal Trig

Functions for (Do not use your summary sheet or notes)