4.2 Graphing trigonometric functions Q2

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Don Shearman

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3 years ago

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Barbara Gunn commented 2 months, 3 weeks ago

In question statement, changed spelling 'Manipluate' to 'Manipulate'

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Don Shearman 3 years, 3 months ago

Created this as a copy of 4.2 Graphing trigonometric functions Q2 (Geogebra version).

Name	Status	Author	Last Modified
4.2 Graphing trigonometric functions Q1	Ready to use	Jim Pettigrew	24/01/2025 05:49
Jim's copy of Movable syringe JavaScript version	draft	Jim Pettigrew	29/06/2021 08:37
4.1 Graphing trigonometric functions Q1	Ready to use	Don Shearman	04/05/2023 02:21
4.2 Graphing trigonometric functions Q2	Ready to use	Don Shearman	25/01/2025 01:10

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Question statement

{app}

The graph of $f(x)=\tan(nx)$ is shown above (with the parameter $n$ restricted to $[1,12]$ ). Manipulate the slider in this graph to vary the value of $n$ and answer the following question.

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			Name	Type	Generated Value

app

jsxgraphboard

HTML node

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
jessiecode(800,500,[-220,5,220,-5],safe("""
​
  yaxis = axis( [0,0],[0,1] ) <<
  ticks: <<
    ticksdistance: 0.5,
    insertticks: false
  >>,
  withLabel: true,
  name: '$f(\\\\theta)$',
  useMathjax: true,
  label: <<position: 'urt', fontSize: 20, offset: [10,0]>>
>>;
    
xaxis = axis( [0,0],[1,0] ) <<
  ticks: <<
    ticksdistance: 45,
    insertticks: false
  >>,
  withLabel: true,
  name: '$\\\\theta$',
  useMathjax: true,
  label: <<position: 'urt', fontSize: 20, offset: [-10,10]>>
>>;
​
  slider([-200,4.5],[-150,4.5],[1,1,12]) <<name:"n", snapWidth: 1, useMathjax: true>>;
    
  functiongraph(function(x){ m=n.Value(); return tan(m*x*PI/180);}, -220, 220) <<highlight: false, strokeWidth: 2>>;
  """),
[
    "axis": false
    
    
    ])

JME function reference

This variable is an interactive HTML node. Interactive HTML nodes can not be relied upon to work correctly when resuming a session - for example, attached event callbacks will be lost, and mathematical notation will likely also break.

If this causes problems, try to create HTML nodes where you use them in content areas, instead of storing them in variables.

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Generated value: `jsxgraphboard`

0,0

$f(\theta)$

$\theta$

n = 1.00

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Statement

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What is the relationship between $n$ and the period of the function?

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Period is $\frac{180}{n}$

Marks: Distractor Message:
Period is $\frac{360}{n}$

Marks: Distractor Message:
Period is $180\times n$

Marks: Distractor Message:
Period is $360\times n$

Marks: Distractor Message:
Period is $n$

Marks: Distractor Message:
Period is $\frac{n}{180}$

Marks: Distractor Message:
Period is $\frac{n}{360}$

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Advice

In general, the period of the function $f(x)=\tan(nx)$ is given by the fomula

\[\text{Period = }\left|\frac{180}{n}\right|,\]

noting that the absolute value function, $|\cdot|$, ensures the period is always a positive number.

In this example, since $n$ is such that $1\leq n \leq 12$, $\frac{180}{n}$ is always positive, so the use of the absolute value function in the period formula is not necessary.

But in a more general example, say $f(x)=\tan(-3x)$, we would have $\text{Period = }\left|\frac{180}{-3}\right|=\left|-\frac{180}{3}\right|=\frac{180}{3}=60.$

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Taxonomy: mathcentre

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Barbara Gunn commented 2 months, 3 weeks ago

Don Shearman 3 years ago

Don Shearman 3 years ago

Don Shearman 3 years, 3 months ago

Error in variable testing condition

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Generated value: `jsxgraphboard`

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4.2 Graphing trigonometric functions Q2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Barbara Gunn commented 2 months, 3 weeks ago

Don Shearman 3 years ago

Don Shearman 3 years ago

Don Shearman 3 years, 3 months ago

Error in variable testing condition

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Generated value: jsxgraphboard

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Generated value: `jsxgraphboard`