Finding exact values for the tangent of the sum or difference of two angles is a little more complicated, but again, it is a matter of recognizing the pattern.
Finding the sum of two angles formula for tangent involves taking quotient of the sum formulas for sine and cosine and simplifying. Recall,
Let’s derive the sum formula for tangent.
We can derive the difference formula for tangent in a similar way.
Sum and difference formulas for tangent
The
sum and difference formulas for tangent are:
Given two angles, find the tangent of the sum of the angles.
Write the sum formula for tangent.
Substitute the given angles into the formula.
Simplify.
Finding the exact value of an expression involving tangent
Find the exact value of
Let’s first write the sum formula for tangent and then substitute the given angles into the formula.
Next, we determine the individual function values within the formula:
We can use the sum and difference formulas to identify the sum or difference of angles when the ratio of sine, cosine, or tangent is provided for each of the individual angles. To do so, we construct what is called a reference triangle to help find each component of the sum and difference formulas.
To find
we begin with
and
The side opposite
has length 3, the hypotenuse has length 5, and
is in the first quadrant. See
[link] . Using the Pythagorean Theorem, we can find the length of side
Since
and
the side adjacent to
is
the hypotenuse is 13, and
is in the third quadrant. See
[link] . Again, using the Pythagorean Theorem, we have
Since
is in the third quadrant,
The next step is finding the cosine of
and the sine of
The cosine of
is the adjacent side over the hypotenuse. We can find it from the triangle in
[link] :
We can also find the sine of
from the triangle in
[link] , as opposite side over the hypotenuse:
Now we are ready to evaluate
We can find
in a similar manner. We substitute the values according to the formula.
For
if
and
then
If
and
then
Then,
To find
we have the values we need. We can substitute them in and evaluate.
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.