Graphing Trigonometric Functions
We have been using the coordinate plane to plot angles, their terminal sides and the unit circle. There is another way to use the coordinate plane to represent trigonometric functions - using the set of points (x, sin(x)) where x is in radians.
Below, plot the points of the form (x, sin(x)) for the x values listed below.
x= 0, π/3, π/4, π/6, π/2, 3π/4, π, 5π/4, 7π/6, 3π/2, 5π/3, 7π/4, 11π/3, 2π
To do that - in the box in the top left type the value of x and the value of sin(x) as a point like (0, 0) using the provided keyboard.
What do you notice about the domain of this function?
What do you notice about the range of this function?
Is this function one to one?
Now enter the function y = sin(x). What do you notice?
Spend some time changing the value of theta and seeing what happens to the graph. What do you think would happen if you could keep increasing theta?
How often will the sine graph have repeat y values?
Do the same for y = cos(x). Compare this graph to the graph of sin(x).
How often will the cosine graph have repeat y values?
The amplitude of the trigonometric function is the half of the distance from the highest y value to the lowest y value.
The period of the trigonometric function is how long before the y values begin to repeat.