Name: Graphical Transformation of Trigonometric Functions
Uploaded: 2019-07-19
Duration: 1 h 7 min 57 s
Description: We love to graph functions, and now that we know about trigonometric functions, these are periodic functions. Let's learn to graph those too!

Question

For the following graph, find the amplitude, frequency, and period. Then, write down the equation that represents the function.

Accepted Answer

We have given the following graph-

We know that the amplitude of a graph is half of the distance between the maximum or minimum value.

So, the amplitude of the given graph $= \frac{4 - (- 4)}{2} = 4$

The period is the horizontal length of one complete cycle as shown in the graph.

So, the period of the graph $= 360 °$ .

The frequency of a curve $= \frac{360 °}{period} = \frac{360 °}{360 °} = 1$ .

Thus, the amplitude, frequency, and period for the given graph are $4, 1$ , and $360 °$ respectively.

The graph is symmetric about the y-axis. So, the general form of the function is: $y = a \cos (b x + c) + d$ , where $a$ is the amplitude of a curve which is half of the distance between the maximum and minimum values, $b$ is the frequency, $c$ is the horizontal shift of the function and $d$ is the displacement in the upward or downward direction of the y-axis.

We have the value of $a = 4, b = 1$

Now, $c = 0$ , and $d = \frac{4 + (- 4)}{2} = \frac{0}{2} = 0$

By substituting the value of $a, b, c$ , and $d$ in the general form of the function, we get-

$\Rightarrow y = 4 \cos (1 . x + 0) + 0 \Rightarrow y = 4 \cos x$

Thus, the equation of the graph is $y = 4 \cos x$ .

For the following graph, find the amplitude, frequency, and period. Then, write down the equation that represents the function.

Important Questions on Trigonometric Functions

Learn and Prepare for any exam you want !