Answers to Question in Tutorial of Sine Function

Answers to the questions in the tutorial of sine function are presented.

Question:
use the scroll bar to set a=1,b=1,c=0 and d=0. Write down f(x) and take note of the amplitude, period and phase shift of f(x)? Now change a , how does it affect the graph? The amplitude is defined as |a|.

Answer:
f(x) = sin(x). The amplitude should be close (in theory equal) to 1. The period should be close (in theory equal) to 2 pi. The phase shift is equal to 0.
As | a | changes the amplitude, which is the maximum value of f(x), changes. In fact this maximum value is equal to | a |.


Question:
Set a=1,c=0,d=0 and change b. Find the period from the graph and compare it to 2pi/|b|. How does b affect the graph of f(x)? The period is the horizontal distance (along the x-axis) between two points: one is the starting point of a cycle and the second is the end point of the same cycle.

Answer:
The measured period should be close (in theory equal) to 2 pi/2. As | b | increases, the graph of f(x) is compressed. As | b | decreases, the graph of f(x) is stretched.


Question:
Set a=1,b=1,d=0 and change c starting from zero going slowly to positive larger values. Take note of the shift, is it left or right?

Answer:
The shift of the graph of f(x) is to the left.


Question:
Set a=1,b=1,d=0 and change c starting from zero going slowly to negative smaller values. Take note of the shift, is it left or right?

Answer:
The shift of the graph of f(x) is to the right.


Question:
repeat the above for b=2,3 and 4, measure the shift and compare it to -c/b (the phase shift).

Answer:
The shift of the graph of f(x) should be close (in theory equal) to -c/b. If
-c/b is positive, the shift is to the left. If -c/b is negative, the shift is to the right.


Question:
Set a,b and c to non zero values and change d. What is the direction of the shift of the graph?

Answer: As d changes, the graph of f(x) is shifted up for values of d > 0 and down for values of d < 0.

More references and links on sine functions.