We can find
coterminal angles measured in radians in much the same way as we have found them using degrees. In both cases, we find coterminal angles by adding or subtracting one or more full rotations.
Given an angle greater than
find a coterminal angle between 0 and
Subtract
from the given angle.
If the result is still greater than
subtract
again until the result is between
and
The resulting angle is coterminal with the original angle.
Finding coterminal angles using radians
Find an angle
that is coterminal with
where
When working in degrees, we found coterminal angles by adding or subtracting 360 degrees, a full rotation. Likewise, in radians, we can find coterminal angles by adding or subtracting full rotations of
radians:
The angle
is coterminal, but not less than
so we subtract another rotation.
Recall that the radian measure
of an angle was defined as the ratio of the
arc length
of a circular arc to the radius
of the circle,
From this relationship, we can find arc length along a circle, given an angle.
Arc length on a circle
In a circle of radius
r , the length of an arc
subtended by an angle with measure
in radians, shown in
[link] , is
Given a circle of radius
calculate the length
of the arc subtended by a given angle of measure
If necessary, convert
to radians.
Multiply the radius
Finding the length of an arc
Assume the orbit of Mercury around the sun is a perfect circle. Mercury is approximately 36 million miles from the sun.
In one Earth day, Mercury completes 0.0114 of its total revolution. How many miles does it travel in one day?
Use your answer from part (a) to determine the radian measure for Mercury’s movement in one Earth day.
Let’s begin by finding the circumference of Mercury’s orbit.
Since Mercury completes 0.0114 of its total revolution in one Earth day, we can now find the distance traveled.
Astronomy (from Ancient Greek ἀστρονομία (astronomía) 'science that studies the laws of the stars') is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution.
Rafael
vjuvu
Elgoog
what is big bang theory?
Rosemary
what type of activity astronomer do?
Rosemary
No
Richard
the big bang theory is a theory which states that all matter was compressed together in one place the matter got so unstable it exploded releasing All its contents in the form of hydrogen
according to the theory of astronomers why the moon is always appear in an elliptical orbit?
Gatjuol
hi !!! I am new in astronomy....
I have so many questions in mind ....
all of scientists of the word they just give opinion only.
but they never think true or false ...
i respect all of them...
I believes whole universe depending
on true ...থিউরি
Govinda
hello
Jackson
hi
Elyana
we're all stars and galaxies a part of sun. how can science prove thx with respect old ancient times picture or books..or anything with respect to present time .but we r a part of that universe
there many theory to born universe but what is the reality of big bang theory to born universe
Asmit
what is the exact value of π?
Nagalakshmi
by big bang
universal
there are many theories regarding this it's on you believe any theory that you think is true ex. eternal inflation theory, oscillation model theory, multiple universe theory the big bang theory etc.
Aarya
I think after Big Bang!
Michele
from where on earth could u observe all the stars during the during the course of an year
is that so. the question was in the end of this chapter
Karuna
in theory, you could see them all from the equator (though over the course of a year, not at pne time). stars are measured in "declination", which is how far N or S of the equator (90* to -90*). Polaris is the North star, and is ALMOST 90* (+89*).
So it would just barely creep over the horizon.
Christopher
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