Chapter 14: Q34. (page 767)

Draw a graph of cosine function with an amplitude of $\frac{7}{8}$ and a period of $\frac{2 π}{5}$ . Then write an equation for the cosine function.

Short Answer

Expert verified

The equation of the cosine function is $y = \frac{7}{8} \cos (5 x)$ .

The amplitude of $y = \frac{7}{8} \cos (5 x)$ is $\frac{7}{8}$ .

The period of $y = \frac{7}{8} \cos (5 x)$ is $\frac{2 π}{5}$ .

Step by step solution

Step 1. Write down the given information.

The given cosine function has an amplitude of $\frac{7}{8}$ and a period of $\frac{2 π}{5}$ .

Step 2. Concept used.

A function of the form $y = a \sin (b x) and y = a \cos (b x)$ has amplitude of $|a|$ and a period of $\frac{360 °}{|b|} or \frac{2 π}{|b|}$ .

Step 3. Write the equation of sine function of given amplitude and period.

Since the given cosine function has an amplitude of $\frac{7}{8}$ and a period of $\frac{2 π}{5}$ . Therefore, plugging $|a| = \frac{7}{8}$ in cosine function $y = a \cos (b x)$ and equating period of cosine function $\frac{2 π}{|b|} = \frac{2 π}{5}$ to get $b = 5$ .

Now, plugging $|a| = \frac{7}{8}$ and $b = 5$ in $y = a \cos (b x)$ . Therefore, the equation of cosine function of given amplitude and period is written as $y = \frac{7}{8} \cos (5 x)$ .

Step 4. Sketch the graph for the obtained function.

The graph for the function $y = \frac{7}{8} \cos (5 x)$ of amplitude $|a| = \frac{7}{8}$ and period $\frac{2 π}{5}$ is shown below.

Step 5. Interpretation from the graph.

The equation of the cosine function is $y = \frac{7}{8} \cos (5 x)$ .

The amplitude of $y = \frac{7}{8} \cos (5 x)$ is $\frac{7}{8}$ .

The period of $y = \frac{7}{8} \cos (5 x)$ is $\frac{2 π}{5}$ .

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Draw a graph of cosine function with an amplitude of $\frac{7}{8}$ and a period of $\frac{2 π}{5}$ . Then write an equation for the cosine function.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Write the equation of sine function of given amplitude and period.

Step 4. Sketch the graph for the obtained function.

Step 5. Interpretation from the graph.

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Draw a graph of cosine function with an amplitude of 78 and a period of 2π5. Then write an equation for the cosine function.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Write the equation of sine function of given amplitude and period.

Step 4. Sketch the graph for the obtained function.

Step 5. Interpretation from the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Discrete Mathematics

Calculus

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Draw a graph of cosine function with an amplitude of $\frac{7}{8}$ and a period of $\frac{2 π}{5}$ . Then write an equation for the cosine function.