Exploring Trigonometric Functions with Autograph
Set Preferences to Advanced level.
Set angle measure to radians.
π
Edit Axes:
set x range to min -12 max 12
set spacing for x numbers to π (Alt P)
1. Enter equation y=sinx
a. What is the period (the length of the section that is repeated)?
b. What is the amplitude (half the difference between min and max
values)?
c. Use the graph (and your knowledge of special angles) to find the
general solution of sinx=1, sinx=0, sinx=-1, sinx=±1/2, sinx=±√3/2,
sinx=±1/√2.
2. Draw graphs of y=2sinx, y=3sinx, y=-sinx, etc.
a. Answer the same (or similar) questions as in q.1.
b. Generalise and explain the relationship between these graphs and
y=sinx.
3. Draw graphs of y=sin2x, y=sin3x, y=sin0.5x, etc.
a. Answer the same (or similar) questions as in q.1.
b. Generalise and explain the relationship between these graphs and
y=sinx.
4. Draw graphs of y=sin(x+π/4), y=sin(x-π/3), y=sin(x+π/2), y=sin(x-π/2),
etc.
a. Answer the same (or similar) questions as in q.1.
b. Generalise and explain the relationship between these graphs and
y=sinx.
Extension:
Try graphing functions composed of sums or products of sin and cos functions,
e.g. y=sinx+cosx, y=(sinx)(cosx). Can you find ‘simple’ trig functions that are
equivalent to compound ones?