Expressing the product of sines in terms of
cosine is also derived from the sum and difference identities for cosine. In this case, we will first subtract the two cosine formulas:
Then, we divide by 2 to isolate the product of sines:
Similarly we could express the product of cosines in terms of sine or derive other product-to-sum formulas.
The product-to-sum formulas
The
product-to-sum formulas are as follows:
Express the product as a sum or difference
Write
as a sum or difference.
We have the product of cosines, so we begin by writing the related formula. Then we substitute the given angles and simplify.
Some problems require the reverse of the process we just used. The
sum-to-product formulas allow us to express sums of sine or cosine as products. These formulas can be derived from the product-to-sum identities. For example, with a few substitutions, we can derive the sum-to-product identity for
sine . Let
and
Then,
Thus, replacing
and
in the product-to-sum formula with the substitute expressions, we have
The other sum-to-product identities are derived similarly.
Sum-to-product formulas
The
sum-to-product formulas are as follows:
Writing the difference of sines as a product
Write the following difference of sines expression as a product:
We begin by writing the formula for the difference of sines.
Substitute the values into the formula, and simplify.
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.