Question

How do you find the amplitude and period of the function $y=6\sin x$?

Answer 1

Now the amplitude of the function is nothing but the maximum value of the function from axis. Hence we will calculate the maximum value to find amplitude. Now we have the period of the function $a\sin \left( b\left( x-c \right) \right)$ is $\dfrac{2\pi }{\left| b \right|}$ . Hence we write the function in the above form find b and then find the period of the function.

Complete step by step solution:
Now the given function is a trigonometric function.
We know that trigonometric functions are periodic functions.
Now let us first find the amplitude of the function.
Amplitude of the function is nothing but the maximum height of the function measured from the axis of the function.
Now we know that the maximum value of $\sin \left( x \right)$ is 1.
Hence we have the maximum value of the function is $6\sin x$ $6\times 1=6$
Hence we have the amplitude of the function is 6.
Now we want to find the period of the function.
We know that the period of the function of the form $a\sin \left( b\left( x-c \right) \right)$ is given by $\dfrac{2\pi }{\left| b \right|}$ .
Now we can write $6\sin \left( x \right)=6\sin \left( 1\left( x-0 \right) \right)$ hence we have b = 1.
Now the period of the function is $2\pi$ .
Hence the amplitude of the function is 6 and the period of the function is $2\pi$ .

Note: Now note that the time period of function is distance after which the function repeats its value. Now we have the formula for time period is $\dfrac{2\pi }{b}$ hence if b > 1 then the period decreases and the function shrinks similarly if the value of b is less than 1 then the function expands.