When working with right triangles, keep in mind that the same rules apply regardless of the orientation of the triangle. In fact, we can evaluate the six trigonometric functions of either of the two acute angles in the triangle in
[link] . The side opposite one acute angle is the side adjacent to the other acute angle, and vice versa.
Many problems ask for all six trigonometric functions for a given angle in a triangle. A possible strategy to use is to find the sine, cosine, and tangent of the angles first. Then, find the other trigonometric functions easily using the reciprocals.
Given the side lengths of a right triangle, evaluate the six trigonometric functions of one of the acute angles.
If needed, draw the right triangle and label the angle provided.
Identify the angle, the adjacent side, the side opposite the angle, and the hypotenuse of the right triangle.
Find the required function:
sine as the ratio of the opposite side to the hypotenuse
cosine as the ratio of the adjacent side to the hypotenuse
tangent as the ratio of the opposite side to the adjacent side
secant as the ratio of the hypotenuse to the adjacent side
cosecant as the ratio of the hypotenuse to the opposite side
cotangent as the ratio of the adjacent side to the opposite side
Evaluating trigonometric functions of angles not in standard position
Finding trigonometric functions of special angles using side lengths
It is helpful to evaluate the trigonometric functions as they relate to the special angles—multiples of
and
Remember, however, that when dealing with right triangles, we are limited to angles between
Suppose we have a
triangle, which can also be described as a
triangle. The sides have lengths in the relation
The sides of a
triangle, which can also be described as a
triangle, have lengths in the relation
These relations are shown in
[link] .
We can then use the ratios of the side lengths to evaluate trigonometric functions of special angles.
Given trigonometric functions of a special angle, evaluate using side lengths.
Use the side lengths shown in
[link] for the special angle you wish to evaluate.
Use the ratio of side lengths appropriate to the function you wish to evaluate.
Evaluating trigonometric functions of special angles using side lengths
Find the exact value of the trigonometric functions of
using side lengths.
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.