Plot the point (-7, -5). We are in quadrant 3.
We also know that tan θ = opp/adj.
Cot θ = adj/opp.
Let us use a^2 + b^2 = r^2 to show you how to find r, the radius aka hypotenuse.
Look: (-7)^2 + (-5)^2 = r^2
If you should ever need to find r, do this:
(-7)^2 + (-5)^2 = r^2
(49) + 25) = r^2
74 = r^2
Take the square root on both sides of the equation to find r.
sqrt{74} = sqrt{r^2}
sqrt{74} = r
It is ok to simplify the sqrt{74} but not needed.
We now have the three sides of the triangle that is form in quadrant 3.
We can now read cot θ from the triangle itself.
So, cot θ = adj/opp = (-7)/(-5) or 7/5.
No need to find r but I simply wanted to show you how it's done in case you are given a question where r must be found.
Answer:
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Hope this helped! :)
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Answer:
You can proceed as follows:
Step-by-step explanation:
First solve the quadratic inequality 
. To do that, factorize, then we have that 
. This implies that
or
In the first case the solution is the empty set 
. In the second case the solution is the interval 
. Now we have that
![A=[1,4]](https://tex.z-dn.net/?f=A%3D%5B1%2C4%5D)
![C=(3,4]](https://tex.z-dn.net/?f=C%3D%283%2C4%5D)
.
To show that 
consider 
. Then 
, this implies that 
, then 
. Now, to show that 
consider , then , then 
, then ![x\in [1,4] \, \text{and}\, x\in (3,5)](https://tex.z-dn.net/?f=x%5Cin%20%5B1%2C4%5D%20%5C%2C%20%5Ctext%7Band%7D%5C%2C%20x%5Cin%20%283%2C5%29)
, this implies that .
Observe the image below.
