Question

1. A sine function has the following key features

Answer 1

Answer:

1) $y= 2sin(\frac{1}{2}x) + 2$

2) $y= 3sin(\frac{\pi}{2}x)-1$

3) $y= 2sin(2x) -2$

Step-by-step explanation:

General form of sin function is

$y= Asin(Bx) + C$

Where A is Amplitude

B is $\frac{2\pi}{\text{Period}}$

C is Mid line

1) Given : A sine function has the following key features  

Frequency = $\frac{1}{4\pi}$

Period is $P=\frac{1}{f}=\frac{1}{\frac{1}{4\pi}}=4\pi$

Amplitude= 2

Mid line y= 2

Y intercept (0,2)  

This function is NOT a reflection of its parent function of the x-axis

Solution : We put the value in the general form of sin function

A= 2 ,  $B=\frac{2\pi}{4\pi}=\frac{1}{2}$ , C=2

$y= Asin(Bx) + C$

$y= 2sin(\frac{1}{2}x) + 2$

2) Given : A sine function has the following key features  

Period = 4

Amplitude = 3

Mid line y = -1

Y intercept (0,-1)

Solution : We put the value in the general form of sin function

A= 3 ,  $B=\frac{2\pi}{4}=\frac{\pi}{2}$ , C=-1

$y= Asin(Bx) + C$

$y= 3sin(\frac{\pi}{2}x)-1$

3) Given : A sine function has the following key features  

Period = $\pi$

Amplitude = 2

Mid line y = -12

Y intercept (0,-2)

Solution : We put the value in the general form of sin function

A= 2 ,  $B=\frac{2\pi}{\pi}=2$ , C=-2

$y= Asin(Bx) + C$

$y= 2sin(2x) -2$