Evaluating compositions of the form
f (
g−1 (
x ))
To evaluate compositions of the form
where
and
are any two of the functions sine, cosine, or tangent and
is any input in the domain of
we have exact formulas, such as
When we need to use them, we can derive these formulas by using the trigonometric relations between the angles and sides of a right triangle, together with the use of Pythagoras’s relation between the lengths of the sides. We can use the Pythagorean identity,
to solve for one when given the other. We can also use the
inverse trigonometric functions to find compositions involving algebraic expressions.
Evaluating the composition of a sine with an inverse cosine
Find an exact value for
Beginning with the inside, we can say there is some angle such that
which means
and we are looking for
We can use the Pythagorean identity to do this.
Since
is in quadrant I,
must be positive, so the solution is
See
[link] .
We know that the inverse cosine always gives an angle on the interval
so we know that the sine of that angle must be positive; therefore
Evaluating the composition of a sine with an inverse tangent
Find an exact value for
While we could use a similar technique as in
[link] , we will demonstrate a different technique here. From the inside, we know there is an angle such that
We can envision this as the opposite and adjacent sides on a right triangle, as shown in
[link] .
Using the Pythagorean Theorem, we can find the hypotenuse of this triangle.
Now, we can evaluate the sine of the angle as the opposite side divided by the hypotenuse.
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life