need help **Identify the period. Do not sketch the graph.**\[ y = \sin \left(\frac{1}{10} x\right) \]---### Explanation:This prompt asks students to identify the period of the sine function $ y = \sin \left(\frac{1}{10} x\right) $.#### Understanding the Period of a Sine Function:- The standard sine function $ y = \sin(x) $ has a period of $ 2\pi $.- When the function is modified to $ y = \sin(bx) $, the period is adjusted by the factor $ b $, and becomes $ \frac{2\pi}{|b|} $.#### Calculation:- In the given function, $ b = \frac{1}{10} $.- Therefore, the period of $ y = \sin \left(\frac{1}{10} x\right) $ is calculated as:\[\frac{2\pi}{\left|\frac{1}{10}\right|} = 20\pi\]Thus, the period of the function $ y = \sin \left(\frac{1}{10} x\right) $ is $ 20\pi $.---A rectangular box is present below the equation, which might be intended for input or display of the calculated period.

given function y=sin110x The general form of sine function can be written as…

Answered: Identify the period. Do not sketch the…

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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**Identify the period. Do not sketch the graph.**

\[ y = \sin \left(\frac{1}{10} x\right) \]

---

### Explanation:

This prompt asks students to identify the period of the sine function $ y = \sin \left(\frac{1}{10} x\right) $.

#### Understanding the Period of a Sine Function:
- The standard sine function $ y = \sin(x) $ has a period of $ 2\pi $.
- When the function is modified to $ y = \sin(bx) $, the period is adjusted by the factor $ b $, and becomes $ \frac{2\pi}{|b|} $.

#### Calculation:
- In the given function, $ b = \frac{1}{10} $.
- Therefore, the period of $ y = \sin \left(\frac{1}{10} x\right) $ is calculated as:

\[
\frac{2\pi}{\left|\frac{1}{10}\right|} = 20\pi
\]

Thus, the period of the function $ y = \sin \left(\frac{1}{10} x\right) $ is $ 20\pi $.

---

A rectangular box is present below the equation, which might be intended for input or display of the calculated period.

Expert Solution

Step 1

given function

$y = \sin \frac{1}{10} x$

The general form of sine function can be written as

$y = a \sin (b x + c) + d w h e r e |a| - a m p l i t u d e \frac{2 π}{b} - p e r i o d - \frac{c}{b} - p h a s e s h i f t d - v e r t i c a l s h i f t$

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