Trig Functions and Graphs Flashcards
Vertical dilation of y=f(x)
y=kf(x) - scale factor k
If k>0
the function is stretched vertically
If 0
the function is compressed vertically
If k = -1
the function is reflected in the x-axis
What is the amplitude
the height from the centre of the periodic function to the maximum or minimum value
What is a horizontal dilation of y = f(x)
y=f(ax) - scale factor 1/a
If a > 0
the function is stretched
If 0<a></a>
the function is compressed
If a = -1
the function is reflected in the y-axis
What is a period
The length of one cycle of a periodic function on the x-axis
Period of cosx and sinx
Given y=sin(ax),
2 π/a
Period of tanx
Given y=tan(ax)
π/a
Vertical translation of y=f(x)
y=f(x) +c
If c>0
centre is translated up
If c<0
centre is translated down
Horizontal translation =
phase shift
What is the phase of y=sin/cos/tan
b:
y=sin(x+b)
y=cos(x+b)
y=tan(x+b)
If b > 0
the phase shift is to the left
If b<0
the phase shift is to the right
What is a phase
angle where x=0 (let x =0 to find phase)
What order to apply transformations in
Start with standard base function (y=sin/cos/tanx)
- Dilations
- Translations
How to solve trig equations graphically
Treat each side of function as a separate function
graph each function separately
solution - x-value where the graphs intersect
How to solve trig equations algebraically
Find the new domain (e.g 2x –> domain=0<2x<720)
Use all stations to central to find all angles in new domain
Find values of x
How to solve trig equations algebraically with a phase shift
Find the new domain by using an inequality with (x+phase) in the centre
Then solve the same way and solve for x, ensuring all angles are in the new domain
What type of functions are sinx and tanx
odd functions (therefore have point symmetry in the origin)
sin(-x)=
-sinx
tan(-x)=
-tanx
What type of function is cosx
even function (therefore has line symmetry in the y-axis)
cos(-x)=
-cosx
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