Question 1195189: I'm stuck on the question,
Find all values of x in the interval [0, 2𝜋] that satisfy the equation. (Enter your answers as a comma-separated list.)
27cot^2(x)=9
Any help would be appreciated, especially a step by step tutorial on how it's done
Answer by ikleyn(52906)   (Show Source):
You can put this solution on YOUR website! .
I'm stuck on the question,
Find all values of x in the interval [0, 2𝜋] that satisfy the equation.
(Enter your answers as a comma-separated list.)
27cot^2(x)=9
Any help would be appreciated, especially a step by step tutorial on how it's done
~~~~~~~~~~~~~~~~~~~
See my step-by-step solution below.
Your starting equation is
27*cot^2(x) = 9
Divide both sides by 27. You will get
cot^2(x) = 
Take square root of both sides
cot(x) = +/-  = +/-  . (1)
It implies that x =  ,  ,  ,  . (2)
If you ask me, how (2) follows from (1), the answer is
that they are the TABLE angles,
which every student must know as he (or she)
knows the multiplication table.
In other words, this knowledge is PRE-REQUISITE
which a student must have starting to solve such problems.
ANSWER. There are 4 values for x. They are , , , .
Solved and explained step by step.
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