describe the transformations that change y = cosx into… y = cos (x-30) y = 3cosx y = -cosx

Transformations

Describe the transformations that change y = cosx into…

y = cos (x-30)

y = 3cosx

y = -cosx

Trigonometry

Aims: To become familiar with the sine, cosine and tangent functions.

Outcomes

Name: To know the sine, cosine and tangent functions.

Describe: The where the sine, cosine and tangent functions come from and sketch their graphs.

Apply transformations to these functions and start to use a graphical calculator to draw them.

Maths

P225 Ex 1A Q2,3 + Revision of C2/C1 Next Lesson: More Trig Graphs and

Functions Hipparchus – Greek Mathematician

(Born in Modern Day Turkey) Discovered the basis of trigonometry c140BC but is more famous for his works in astronomy.

Trig it’s all about________

Generating the Graphs

Visual Demonstrations of sine and cosine from the unit circle.

http://integralmaths.org/course/view.php?id=33

Graphs and Transformations

The same transformation rules we have seen so far can be applied to these graphs. You must be aware of how these graphs influence key elements/ properties.

E.g.

Matchings

Using the transparencies match the functions to the graphs.

Properties - Autograph

Ampiltude: Max/Min: Period (Stretches): Osscilates About:

•Amplitude = 1

•Period = 120°

•Oscillates about 0

•Amplitude = 2

•Period = 90°

•Oscillates about 0

•Amplitude = 4

•Period = 1080°

•Oscillates about 0

•Amplitude = 4

•Period = 180°

•Oscillates about -3

•Amplitude = 2

•Period = 6°

•Oscillates about 5

•Amplitude = 10

•Period = 100°

•Oscillates about 12

Sketch

y=sinx

y=cosx

Homework

Transformations, Trig Graphs and Radians Task

Mathematician: c500CE this Indian Mathematician

that first considered the trigonometric ratios sine and cosine as functions.

Easier Max/Min

How do you identify the maximum and minimum values of trigonometric functions involving sine and cosine...

E.g. What are the maximum and minimum values of 4+2sinx?

Write The Maximum and Minimum Values of...

x2cos85

Write The Maximum and Minimum Values of...

xsin3

8

Write The Maximum and Minimum Values of...

)204sin(9 x

Write The Maximum and Minimum Values of...

xcos2

30

Getting A Tan

Using Symmetry

Given sinx=0.23 and 0≤x≤360 what are the possible values of x?

Use calc to get principle value…

Finding Values

Given sinx=0.23 and 0≤x≤360 what are the possible values of x?

Use graph to find further values…

cosx=0.74 and 0≤x≤360

tanx=5 and 0≤x≤360

Things to Recall Graphs

Use of GDC

Graph Mode – All Powerful!

Transformations Round-Up

Transformations Round-Up

Transformations Round-Up

Transformations Round-Up

Transformations Round-Up