Evaluating compositions of the form
f (
f−1 (
y )) and
f−1 (
f (
x ))
For any trigonometric function,
for all
in the proper domain for the given function. This follows from the definition of the inverse and from the fact that the range of
was defined to be identical to the domain of
However, we have to be a little more careful with expressions of the form
Compositions of a trigonometric function and its inverse
Is it correct that
No. This equation is correct if
belongs to the restricted domain
but sine is defined for all real input values, and for
outside the restricted interval, the equation is not correct because its inverse always returns a value in
The situation is similar for cosine and tangent and their inverses. For example,
Given an expression of the form f
−1 (f(θ)) where
evaluate.
If
is in the restricted domain of
If not, then find an angle
within the restricted domain of
such that
Then
Evaluating compositions of the form
f−1 (
g (
x ))
Now that we can compose a trigonometric function with its inverse, we can explore how to evaluate a composition of a trigonometric function and the inverse of another trigonometric function. We will begin with compositions of the form
For special values of
we can exactly evaluate the inner function and then the outer, inverse function. However, we can find a more general approach by considering the relation between the two acute angles of a right triangle where one is
making the other
Consider the sine and cosine of each angle of the right triangle in
[link] .
Because
we have
if
If
is not in this domain, then we need to find another angle that has the same cosine as
and does belong to the restricted domain; we then subtract this angle from
Similarly,
so
if
These are just the function-cofunction relationships presented in another way.
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.