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

##### 1 Answer

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 $\sin x$ into the function.
You know, $- 1 \setminus \le q \sin x \setminus \le q + 1$

So,
The smallest value of the function, $y = - 5 \sin x$ $= - 5 \setminus \times - 1 = + 5$
The largest value of the function $= - 5 \setminus \times + 1 = - 5$

So, the Range= $\left[- 5 , + 5\right]$
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 $\sin x$ . 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, ${P}_{f} = \setminus \frac{{P}_{l}}{2 \setminus \pi}$
Period, $P = \setminus \frac{{P}_{f}}{c}$
Combining Them you get,
${P}_{f} = \setminus \frac{{P}_{l}}{2 \setminus \pi c}$
For your given function, $y = - 5 \sin x$
${P}_{l} = 2 \setminus \pi$
$c = 1$

So, Period of the function $= \setminus \frac{2 \setminus \pi}{2 \setminus \pi \setminus \times 1}$
$= 1$

A piece of cake isn't it?

Now can you say the Amplitude and Period of this function?
$y = \setminus \frac{24}{7} \cos 4 x$

Happy Problem Solving!!!