# Horizontal Shift

 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 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 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 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       # Horizontal Shift

###### Adding a constant to 'x' translates the graph horizontally Mouse-over the equations to see the graph translation       