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