Answer
Verified
362.4k+ views
Hint: First, the general equation of wave has to be known. Since the sinusoidal equation is given, the general equation should also be sinusoidal. The amplitude is the highest displacement of the wave that we can get from the general equation. Also, the period, phase shift, and vertical displacement are noted in that equation. The given equation has to be equated with the general one to find the values of required amplitude, period, phase, and vertical displacement.
Formula used:
The general equation: $y = a\sin (px - q) + r$
Where, $a = $ amplitude
$r = $ the vertical shift.
$\dfrac{{2\pi }}{p} = $ period.
$q = $ the phase shift.
Complete answer:
The given equation is, $y = \sin x - 1$
Clearly, it is a sinusoidal equation.
The general equation of wave is to take here, $y = a\sin (px - q) + r$
Where, $a = $ amplitude
$r = $ the vertical shift.
$\dfrac{{2\pi }}{p} = $ period.
$q = $ the phase shift.
If we write $y = \sin x - 1$ as $y = a\sin (px - q) + r$, it will be like:
$y = 1.\sin (1.x - 0) + ( - 1)$
By equating with the general equation we get from $y = 1.\sin (1.x - 0) + ( - 1)$,
$a = 1$, $p = 1$, $q = 0$ , $r = - 1$
Therefore, the amplitude $a = 1$
The period,$\dfrac{{2\pi }}{p} = \dfrac{{2\pi }}{1} = 2\pi $
The phase shift, $q = 0$
The vertical displacement, $r = - 1$
Note:
$y = \sin x - 1$ - This function is the same as $y = \sin x$ except it starts from $( - 1)$ rather than zero.
Also, the amplitude$\left( {a = 1} \right)$ is the same as that of the function $y = \sin x$ and the period$(2\pi )$ is similar to that of the function $y = \sin x$.
For the equation when there is $\sin x,\cos x,\sec x$ we take the period $2\pi $ and for the equation when there is $\tan x,\cot x$ we take the period $\pi $.
The phase shift we get here is, $q = 0$which means there is no shift in left or right.
The vertical displacement, $r = - 1$, which means the value of the function at $x = 0$.
Formula used:
The general equation: $y = a\sin (px - q) + r$
Where, $a = $ amplitude
$r = $ the vertical shift.
$\dfrac{{2\pi }}{p} = $ period.
$q = $ the phase shift.
Complete answer:
The given equation is, $y = \sin x - 1$
Clearly, it is a sinusoidal equation.
The general equation of wave is to take here, $y = a\sin (px - q) + r$
Where, $a = $ amplitude
$r = $ the vertical shift.
$\dfrac{{2\pi }}{p} = $ period.
$q = $ the phase shift.
If we write $y = \sin x - 1$ as $y = a\sin (px - q) + r$, it will be like:
$y = 1.\sin (1.x - 0) + ( - 1)$
By equating with the general equation we get from $y = 1.\sin (1.x - 0) + ( - 1)$,
$a = 1$, $p = 1$, $q = 0$ , $r = - 1$
Therefore, the amplitude $a = 1$
The period,$\dfrac{{2\pi }}{p} = \dfrac{{2\pi }}{1} = 2\pi $
The phase shift, $q = 0$
The vertical displacement, $r = - 1$
Note:
$y = \sin x - 1$ - This function is the same as $y = \sin x$ except it starts from $( - 1)$ rather than zero.
Also, the amplitude$\left( {a = 1} \right)$ is the same as that of the function $y = \sin x$ and the period$(2\pi )$ is similar to that of the function $y = \sin x$.
For the equation when there is $\sin x,\cos x,\sec x$ we take the period $2\pi $ and for the equation when there is $\tan x,\cot x$ we take the period $\pi $.
The phase shift we get here is, $q = 0$which means there is no shift in left or right.
The vertical displacement, $r = - 1$, which means the value of the function at $x = 0$.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
10 examples of evaporation in daily life with explanations
Write a letter to the principal requesting him to grant class 10 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Name 10 Living and Non living things class 9 biology CBSE