Question

How do you find the amplitude and period of `y= -5sinx`?

Answer 1

Amplitude : `5`
Period : `1`

Explanation:

A little explanation would be quite adequate for this problem.

1. To determine the Amplitude, put the smallest and largest values of `sinx` into the function.
   You know, `-1\leq sinx\leq +1`

So,
The smallest value of the function, `y= -5sinx` `= -5\times-1= +5`
The largest value of the function `= -5\times+1= -5`

So, the Range= `[-5,+5]`
As amplitude is equal to the largest value of the Range,
Amplitude =`5`
Notice that [] braces. It carries some important information!

1. Now, look at the `sinx` . Identity the Coefficient of the angle, x.
   Assume,
   The fundamental period `=P_f`
   Fundamental period length`=P_l`
   Coefficient of angle, x `=c`
   Now,
   Two shorty, golden equation for you,
   Fundamental Period, `P_f=\frac{P_l}{2\pi}`
   Period, `P=\frac{P_f}{c}`
   Combining Them you get,
   `P_f=\frac{P_l}{2\pic}`
   For your given function, `y= -5sinx`
   `P_l=2\pi`
   `c=1`

So, Period of the function `=\frac{2\pi}{2\pi\times1}`
`=1`

A piece of cake isn't it?

Now can you say the Amplitude and Period of this function?
`y=\frac{24}{7} cos4x`

Happy Problem Solving!!!