Question

What is the amplitude of the function $y = - 3\sin x$?

Answer 1

Hint : Here in this question, we have to find the amplitude of a given trigonometric sine function. For this, we need to compare the given equation by the standard form i.e., $a\sin \left( {bx - c} \right) + d$ here, to find the amplitude = $\left| a \right|$ by taking a mod value we get the required solution.

Complete step by step solution:
Amplitude is the height from the centre line to the peak (or to the trough). Or we can measure the height from highest to lowest points and divide that by 2.
Let us use the standard or general form of sinusoidal functions as $a\sin \left( {bx - c} \right) + d$ .
Where,
$\left| a \right|$ be the amplitude
‘b’ be the number of cycles from 0 to $2\pi$
‘d’ be the vertical shift
‘c’ is the horizontal shift.
on comparing the variables used to find the amplitude, and period.
Now consider the given expression
$y = - 3\sin x$
Here,
a = -3
b = 1
c = 0
d = 0
To Find the amplitude = $\left| a \right|$.
$\Rightarrow \,\,$Amplitude $= \left| a \right| = \left| { - 3} \right| = 3$
Hence, the amplitude of the function $y = - 3\sin x$ is 3.
So, the correct answer is “3”.

Note : The period is the length of the smallest interval that contains exactly one copy of the repeating pattern. The Amplitude is the height from the centre line to the peak. We use the form of the equation i.e., $a\sin \left( {bx - c} \right) + d$ and we have formulas for the period and amplitude and hence we determine the values. Remember, amplitude is a measure of distance and therefore is always positive.