Fernando Revilla said:If $0<x<45º$,
$$0<\tan x <1\text{ and }0<\tan x<\cot x,\text{ so }t_2=(\tan x)^{\cot x}<(\tan x)^{\tan x}=t_1$$
$$1<\cot x,\text{ so }t_3=(\cot x)^{\tan x}<(\cot x)^{\cot x}=t_4.$$
$$0<\tan x<\cot x,\text{ so }t_1=(\tan x)^{\tan x}<(\cot x)^{\tan x}=t_3.$$
We conclude, $t_2<t_1<t_3<t_4.$
The purpose of arranging t_1, t_2, t_3 and t_4 in decreasing order is to organize the data in a more meaningful way. This allows for easier analysis and comparison of the values. It also helps to identify the highest and lowest values in the set.
The order of t_1, t_2, t_3 and t_4 is determined by their numerical values. The highest value should be placed first, followed by the second highest, and so on. This creates a descending order from highest to lowest.
Yes, t_1, t_2, t_3 and t_4 can be arranged in any order, including ascending or random order. However, arranging them in decreasing order is a common and useful way to organize the data.
If t_1, t_2, t_3 and t_4 have the same value, they can be arranged in any order without affecting the overall result. It is up to the researcher to decide which order is most suitable for their analysis.
No, arranging data in decreasing order is not necessary for all types of analysis. However, it can be a helpful way to organize data for certain types of analysis, such as identifying outliers or determining the top or bottom performers in a dataset.