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.
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ma management ho
Amisha
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
belatari
Amisha
1st year ho
Amisha
nd u
Amisha
ahh
Amisha
kaha biratnagar
Amisha
ys
Amisha
kina k vo
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.