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Nayland College - Mathematics

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Horizontal Shift

Graphs HOME | Achievement Objectives | Parabola Graphs | Parabola Questions | Cubics | Hyperbola | Circles | Exponential | Logs | Radians | Trig Graphs Overview | Trig Vertical Shift | Trig Horizontal Shift | Trig Equations | Trig Models | General Translations | Applications | Revision

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Horizontal compression and multiple solutions

When a trig functions has been horizontally compressed eg y = Cos(3x) then there will be multiple solutions (usually 2 solutions in the range 0 to 360 degrees) or 0 < x < 2π
Using the graph method and the unit circle with repeated revolutions to find all solutions (in degrees and radians)


Class Notes | Blank Notes

Ex 35.05 and Ex 35.06

Horizontal transformations

Transformation in Degrees: Sin graph | Cos Graph | Tan_Graph

Transformation in Radians: Sin graph | Cos Graph | Tan Graph

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Horizontal Translation

The basic trig functions can be translated horizontally eg y = Tan(x + 1.2) Solve the equivalent function y = Tan(A) where 'A' = x + 1.2
Sketching translated functions.

Solving two step problems involving horizontal translation using the graph method and unit circle method


Class Notes | Blank Notes

Graphing Ex 35.02 #9 to 13,
#17 to 20 and
Ex 35.03 #4 & 11

Solving Ex 35.04

3 step problems

p158 & p156

Horizontal transformations

Solving two step problems

 

Multiply x by a number (n) produces 'n' cycles in 360 (or 2pi)

Mouse-over the equations to see the graph translation

Transformation in Degrees: Sin graph | Cos Graph | Tan Graph

Transformation in Radians: Sin graph | Cos Graph | Tan Graph

 

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Horizontal Shift

Adding a constant to 'x' translates the graph horizontally



Mouse-over the equations to see the graph translation

 

Mixed transformations (web link)
http://www.bbc.co.uk/schools/gcsebitesize/maths/activities/sine.shtml
http://www.bbc.co.uk/schools/gcsebitesize/maths/activities/cosine.shtml

 

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