Answers to Question in Tutorial of Sine Function

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

Question:

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

Tutorial on Sine Functions (1)- Problems.
Tutorial on Sine Functions (2)- Problems.
Graph of Sine, a*sin(bx+c), Function.

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