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Home
- Algebra and trigonometry
- The unit circle: sine and cosine
- Unit circle
Key equations
Cosine |
|
Sine |
|
Pythagorean Identity |
|
Key concepts
- Finding the function values for the sine and cosine begins with drawing a unit circle, which is centered at the origin and has a radius of 1 unit.
- Using the unit circle, the sine of an angle
equals the
y -value of the endpoint on the unit circle of an arc of length
whereas the cosine of an angle
equals the
x -value of the endpoint. See
[link] .
- The sine and cosine values are most directly determined when the corresponding point on the unit circle falls on an axis. See
[link] .
- When the sine or cosine is known, we can use the Pythagorean Identity to find the other. The Pythagorean Identity is also useful for determining the sines and cosines of special angles. See
[link] .
- Calculators and graphing software are helpful for finding sines and cosines if the proper procedure for entering information is known. See
[link] .
- The domain of the sine and cosine functions is all real numbers.
- The range of both the sine and cosine functions is
- The sine and cosine of an angle have the same absolute value as the sine and cosine of its reference angle.
- The signs of the sine and cosine are determined from the
x - and
y -values in the quadrant of the original angle.
- An angle’s reference angle is the size angle,
formed by the terminal side of the angle
and the horizontal axis. See
[link] .
- Reference angles can be used to find the sine and cosine of the original angle. See
[link] .
- Reference angles can also be used to find the coordinates of a point on a circle. See
[link] .
Section exercises
Verbal
Discuss the difference between a coterminal angle and a reference angle.
Coterminal angles are angles that share the same terminal side. A reference angle is the size of the smallest acute angle,
formed by the terminal side of the angle
and the horizontal axis.
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Algebraic
For the following exercises, use the given sign of the sine and cosine functions to find the quadrant in which the terminal point determined by
lies.
For the following exercises, find the exact value of each trigonometric function.
Questions & Answers
Ayele, K., 2003. Introductory Economics, 3rd ed., Addis Ababa.
can you send the book attached ?
Ariel
the study of how humans make choices under conditions of scarcity
AI-Robot
U(x,y) = (x×y)1/2
find mu of x for y
U(x,y) = (xÃy)1/2
find mu of x for y
Desalegn
this is the study of how the society manages it's scarce resources
Belonwu
macroeconomic is the branch of economics which studies actions, scale, activities and behaviour of the aggregate economy as a whole.
husaini
difference between firm and industry
what's the difference between a firm and an industry
Abdul
firm is the unit which transform inputs to output where as industry contain combination of firms with similar production 😅😅
Abdulraufu
Suppose the demand function that a firm faces shifted from
Qd 120 3P
to
Qd 90 3P
and the supply function has shifted from
QS
20 2P
to
QS
10 2P .
a) Find the effect of this change on price and quantity.
b) Which of the changes in demand and supply is higher?
explain standard reason why economic is a science
factors influencing supply
scares
means__________________ends
resources. unlimited
Jan
economics is a science that studies human behaviour as a relationship b/w ends and scares means which have alternative uses
Jan
calculate the profit maximizing for demand and supply
Why qualify 28 supplies
Milan
out-of-pocket costs for a firm, for example, payments for wages and salaries, rent, or materials
AI-Robot
concepts of supply in microeconomics
identify a demand and a supply curve
there's a difference
Aryan
Demand curve shows that how supply and others conditions affect on demand of a particular thing and what percent demand increase whith increase of supply of goods
Israr
Hi Sir please how do u calculate Cross elastic demand and income elastic demand?
Abari
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Source:
OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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