Trig Graphs
• Investigate the effects of
• 2sin(x), 2cos(x), 2tan(x)
• sin(2x), cos(2x), tan(2x)
• sin(x)+1, cos(x)+1, tan(x)+1
• - sin(x), - cos(x), - tan(x)
• sin(x-30),cos(x-30),tan(x-30)
2sin(x), 2cos(x), 2tan(x)
The 2sin(x) and 2cos(x)
graphs are obviously twice
as high, but still centred
around the x-axis.
The 2tan(x) graph does not
show as marked a
difference, but does appear
slightly steeper.
sin(2x), cos(2x), tan(2x)
Sin(x) and Cos(x) both complete a cycle
in 360 degrees.
Sin(2x) and Cos(2x) both complete a
cycle in 180 degrees.
The amplitude remains the same.
The (2x) completes a cycle in 1/2 the
time, while (3x) completes in 1/3 the
time.
Tan(x) completes a cycle in 180
degrees.
Tan(2x) completes a cycle in 90
degrees.
sin(x)+1, cos(x)+1, tan(x)+1
The sin(x)+1 and cos(x)+1 graphs
are moved vertically by 1.
If the sign is negative, the graph
would be moved down by that
amount.
Adding +1 and moving the tan
graph up by 1 appears to make little
difference.
- sin(x), - cos(x), - tan(x)
The – sign in front of the sin or
cos graph inverts the graph
about the x axis, but does not
alter the number of waves in
3600 or the altitude of the wave.
The – sign in front of the tan
graph also inverts the function
about the x axis.
sin(x-30), cos(x-30), tan(x-30)
The effect of the -30 is to shift
the graph horizontally 300 in the
opposite direction to what
would seem logical i.e.
positive(right).
If the function was sin(x+30)
then the graph would be shifted
by 300 in the negative direction
(left).
This has the same visual effect
across sin, cos and tan.
Trig Graph Summary
Function
2sin(x), 2cos(x), 2tan(x)
Effect
Twice as high
sin(2x), cos(2x), tan(2x)
Twice as frequent
sin(x)+1, cos(x)+1, tan(x)+1
Shift Vertically
- sin(x), - cos(x), - tan(x)
Invert
sin(x-30), cos(x-30), tan(x-30)
Shift Horiz (+left)(-right)