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

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!!!