Angles in the Coordinate Plane - Pre-Calculus
Card 1 of 44
Convert 
radians to degrees.
Convert
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Write the conversion factor between radians and degrees.
Cancel the radians unit by using dimensional analysis.
Write the conversion factor between radians and degrees.
Cancel the radians unit by using dimensional analysis.
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Convert 
to degrees.
Convert
Tap to reveal answer
Write the conversion factor of radians and degrees.
Substitute the degree measure into 
.
Write the conversion factor of radians and degrees.
Substitute the degree measure into
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Determine the angle 
in degres made in the plane by connecting a line segment from the origin to 
.
Assume 
Determine the angle
Assume
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Firstly, since the point 
is in the 3rd quadrant, it'll be between 
and 
. If we take 
to be the horizontal, we can form a triangle with base and leg of values 
and 
. Solving for the angle in the 3rd quadrant given by 
,
Since this angle is made by assuming 
to be the horizontal, the total angle measure 
is going to be:
Firstly, since the point
Since this angle is made by assuming
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Find the degree measure of 
radians. Round to the nearest integer.
Find the degree measure of
Tap to reveal answer
In order to solve for the degree measure from radians, replace the 
radians with 180 degrees.
The nearest degree is 
.
In order to solve for the degree measure from radians, replace the
The nearest degree is
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Given a triangle, the first angle is three times the value of the second angle. The third angle is 
. What is the value of the second largest angle in degrees?
Given a triangle, the first angle is three times the value of the second angle. The third angle is
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A triangle has three angles that will add up to 
degrees.
Convert the radians angle to degrees by substituting 
for every 
.
The third angle is 60 degrees.
Let the second angle be 
. The first angle three times the value of the second angle is 
. Set up an equation that sums the three angles to 
.
Solve for 
.
Substitute 
for the first angle and second angle.
The second angle is: 
The first angle is: 
The three angles are: 
The second highest angle is: 
A triangle has three angles that will add up to
Convert the radians angle to degrees by substituting
The third angle is 60 degrees.
Let the second angle be
Solve for
Substitute
The second angle is:
The first angle is:
The three angles are:
The second highest angle is:
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Find the coterminal angle of 15 degrees.
Find the coterminal angle of 15 degrees.
Tap to reveal answer
The coterminal angles can be positive or negative. To find the coterminal angles, simply add or subtract 360 degrees as many times as needed from the reference angle.
All of these angles are coterminal angles.
The coterminal angles can be positive or negative. To find the coterminal angles, simply add or subtract 360 degrees as many times as needed from the reference angle.
All of these angles are coterminal angles.
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Of the given answers, what of the following is a coterminal angle of 
radians?
Of the given answers, what of the following is a coterminal angle of
Tap to reveal answer
To find the coterminal angle of an angle, simply add or subtract 
radians, or 360 degrees as many times as needed.
These are all coterminal angles to 
radians.
Out of the given answers, 
is the only possible answer.
To find the coterminal angle of an angle, simply add or subtract
These are all coterminal angles to
Out of the given answers,
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Find the coterminal angle of 
, if possible.
Find the coterminal angle of
Tap to reveal answer
In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.
The only correct answer is 
.
In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.
The only correct answer is
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Of the following choices, find a coterminal angle of 
.
Of the following choices, find a coterminal angle of
Tap to reveal answer
In order to find a coterminal angle, simply add or subtract 
radians to the given angle as many times as possible.
The possible angles after adding increments of 
radians are:
The possible angles after subtracting decrements of 
radians are:
Out of the given possibilities, only 
is a valid answer.
In order to find a coterminal angle, simply add or subtract
The possible angles after adding increments of
The possible angles after subtracting decrements of
Out of the given possibilities, only
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Find the coterminal angle of 15 degrees in standard position from the following answers.
Find the coterminal angle of 15 degrees in standard position from the following answers.
Tap to reveal answer
To determine the coterminal angle, simply add or subtract increments or decrements of 360 degrees to the given angle.
For 
:
These angles can all be coterminal to 15 degrees. The only answer is 
.
To determine the coterminal angle, simply add or subtract increments or decrements of 360 degrees to the given angle.
For
These angles can all be coterminal to 15 degrees. The only answer is
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Which of the following angles is coterminal to 
?
Which of the following angles is coterminal to
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Which of the following angles is coterminal to 
?
Coterminal angles are angles which start and end at the same point. In other words, they share both their starting and ending point. Note, this doesn't require them to be the same angle.
For instance, 
is coterminal with 
, because they both start on the positive x-axis, and end at the same place in quadrant 2.
So, we want to find an angle that ends at the same place in quadrant 1 as 
. Of the answer choices, only 1 ends in quadrant 1, so that one must be our answer: 
Which of the following angles is coterminal to
Coterminal angles are angles which start and end at the same point. In other words, they share both their starting and ending point. Note, this doesn't require them to be the same angle.
For instance,
So, we want to find an angle that ends at the same place in quadrant 1 as
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Convert radians to degrees.
Convert
Tap to reveal answer
Write the conversion factor between radians and degrees.
Cancel the radians unit by using dimensional analysis.
Write the conversion factor between radians and degrees.
Cancel the radians unit by using dimensional analysis.
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Convert to degrees.
Convert
Tap to reveal answer
Write the conversion factor of radians and degrees.
Substitute the degree measure into .
Write the conversion factor of radians and degrees.
Substitute the degree measure into
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Determine the angle in degres made in the plane by connecting a line segment from the origin to .
Assume
Determine the angle
Assume
Tap to reveal answer
Firstly, since the point is in the 3rd quadrant, it'll be between and . If we take to be the horizontal, we can form a triangle with base and leg of values and . Solving for the angle in the 3rd quadrant given by ,
Since this angle is made by assuming to be the horizontal, the total angle measure is going to be:
Firstly, since the point
Since this angle is made by assuming
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Find the degree measure of radians. Round to the nearest integer.
Find the degree measure of
Tap to reveal answer
In order to solve for the degree measure from radians, replace the radians with 180 degrees.
The nearest degree is .
In order to solve for the degree measure from radians, replace the
The nearest degree is
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Given a triangle, the first angle is three times the value of the second angle. The third angle is . What is the value of the second largest angle in degrees?
Given a triangle, the first angle is three times the value of the second angle. The third angle is
Tap to reveal answer
A triangle has three angles that will add up to degrees.
Convert the radians angle to degrees by substituting for every .
The third angle is 60 degrees.
Let the second angle be . The first angle three times the value of the second angle is . Set up an equation that sums the three angles to .
Solve for .
Substitute for the first angle and second angle.
The second angle is:
The first angle is:
The three angles are:
The second highest angle is:
A triangle has three angles that will add up to
Convert the radians angle to degrees by substituting
The third angle is 60 degrees.
Let the second angle be
Solve for
Substitute
The second angle is:
The first angle is:
The three angles are:
The second highest angle is:
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Find the coterminal angle of 15 degrees.
Find the coterminal angle of 15 degrees.
Tap to reveal answer
The coterminal angles can be positive or negative. To find the coterminal angles, simply add or subtract 360 degrees as many times as needed from the reference angle.
All of these angles are coterminal angles.
The coterminal angles can be positive or negative. To find the coterminal angles, simply add or subtract 360 degrees as many times as needed from the reference angle.
All of these angles are coterminal angles.
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Of the given answers, what of the following is a coterminal angle of radians?
Of the given answers, what of the following is a coterminal angle of
Tap to reveal answer
To find the coterminal angle of an angle, simply add or subtract radians, or 360 degrees as many times as needed.
These are all coterminal angles to radians.
Out of the given answers, is the only possible answer.
To find the coterminal angle of an angle, simply add or subtract
These are all coterminal angles to
Out of the given answers,
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Find the coterminal angle of , if possible.
Find the coterminal angle of
Tap to reveal answer
In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.
The only correct answer is .
In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.
The only correct answer is
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Of the following choices, find a coterminal angle of .
Of the following choices, find a coterminal angle of
Tap to reveal answer
In order to find a coterminal angle, simply add or subtract radians to the given angle as many times as possible.
The possible angles after adding increments of radians are:
The possible angles after subtracting decrements of radians are:
Out of the given possibilities, only is a valid answer.
In order to find a coterminal angle, simply add or subtract
The possible angles after adding increments of
The possible angles after subtracting decrements of
Out of the given possibilities, only
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