Chapter 14: Q33. (page 767)

Draw a graph of sine function with an amplitude of $\frac{3}{5}$ and a period of $90 °$ . Then write an equation for the sine function.

Short Answer

Expert verified

The equation of the sine function is $y = \frac{3}{5} \sin (4 x)$ .

The amplitude of $y = \frac{3}{5} \sin (4 x)$ is $\frac{3}{5}$ .

The period of $y = \frac{3}{5} \sin (4 x)$ is $90 °$ .

Step by step solution

Step 1. Write down the given information.

The given sine function has an amplitude of $\frac{3}{5}$ and a period of $90 °$ .

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 sine function has an amplitude of $\frac{3}{5}$ and a period of $90 °$ . Therefore, plugging $|a| = \frac{3}{5}$ in sine function $y = a \sin (b x)$ and equating period of sine function $\frac{360 °}{|b|} = 90 °$ to get $b = 4$ .

Now, plugging $|a| = \frac{3}{5}$ and $b = 4$ in $y = a \sin (b x)$ . Therefore, the equation of sine function of given amplitude and period is written as $y = \frac{3}{5} \sin (4 x)$ .

Step 4. Sketch the graph for the obtained function.

The graph for the function $y = \frac{3}{5} \sin (4 x)$ of amplitude $|a| = \frac{3}{5}$ and period $90 °$ is shown below.

Step 5. Interpretation from the graph.

The equation of the sine function is $y = \frac{3}{5} \sin (4 x)$ .

The amplitude of $y = \frac{3}{5} \sin (4 x)$ is $\frac{3}{5}$ .

The period of $y = \frac{3}{5} \sin (4 x)$ is $90 °$ .

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Draw a graph of sine function with an amplitude of $\frac{3}{5}$ and a period of $90 °$ . Then write an equation for the sine 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 sine function with an amplitude of 35 and a period of 90°. Then write an equation for the sine 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

Discrete Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Statistics

Mechanics Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

Draw a graph of sine function with an amplitude of $\frac{3}{5}$ and a period of $90 °$ . Then write an equation for the sine function.