Unit Circle - Trigonometry
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What point corresponds to an angle of 
radians on the unit circle?
What point corresponds to an angle of
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The unit circle is the circle of radius one centered at the origin 
in the Cartesian coordinate system. 
radians is equivalent to 
. This is a full circle 
plus a quarter-turn 
more. So, the angle 
corresponds to the point 
on the unit circle.
The unit circle is the circle of radius one centered at the origin
What point corresponds to the angle 
on the unit circle?
What point corresponds to the angle
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The unit circle is the circle of radius one centered at the origin 
in the Cartesian coordinate system. 
is equivalent to 
which corresponds to the point 
on the unit circle.
The unit circle is the circle of radius one centered at the origin
Give the angle between 
and 
that corresponds to the point 
.
Give the angle between
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The angle 
or 
corresponds to the point 
.
The angle
What point corresponds to the angle 
on the unit circle?
What point corresponds to the angle
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In order to find the point corresponds to the angle 
on the unit circle we can write:
In the unit circle which has the radious of 
we can write:
So the point corresponds to the angle 
on the unit circle is 
In order to find the point corresponds to the angle
In the unit circle which has the radious of
So the point corresponds to the angle
What point corresponds to the angle 
on the unit circle?
What point corresponds to the angle
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The unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system. 
is equivalent to 
which corresponds to the point 
on the unit circle.
The unit circle is the circle of radius one centered at the origin
What point corresponds to an angle of 
on the unit circle?
What point corresponds to an angle of
Tap to see back →
The unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system. 
is a full circle plus a 
more. So, the angle 
corresponds to the point 
on the unit circle.
The unit circle is the circle of radius one centered at the origin
Which of the following points is NOT on the unit circle?
Which of the following points is NOT on the unit circle?
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For a point to be on the unit circle, it has to have a radius of one. Therefore, the sum of the squares of point's coordinates must also equal one.
Let's try the point 
.
Therefore, this point is not on the unit circle.
For a point to be on the unit circle, it has to have a radius of one. Therefore, the sum of the squares of point's coordinates must also equal one.
Let's try the point
Therefore, this point is not on the unit circle.
When looking at the unit circle, what are the coordinates for an angle of 
?
When looking at the unit circle, what are the coordinates for an angle of
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The coordinates of the point on the circle for each angle are 
.
Since 
and 
, the point will be 
.
The coordinates of the point on the circle for each angle are
Since
What is the radius of the unit circle?
What is the radius of the unit circle?
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By definition, the radius of the unit circle is 1.
By definition, the radius of the unit circle is 1.
What must be the area of the unit circle?
What must be the area of the unit circle?
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The unit circle must have a radius of 1.
Use the circular area formula to find the area.
The unit circle must have a radius of 1.
Use the circular area formula to find the area.
Suppose there is exists an angle, 
such that 
.
For what values of 
and 
make this trigonometric ratio possible?
Suppose there is exists an angle,
For what values of
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The only values such that
are at the values:
This means that the only choice for 
is 
. 
or 
achieve the necessary angles to satisfy this trigonometric ratio.
The only values such that
are at the values:
This means that the only choice for
If 
, and 
, what is 
?
If
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The tangent of an angle yields the ratio of the opposite side to the adjacent side.
If this ratio is 
, we can see that this is a Pythagorean triple (3-4-5); the absolute value of the sine of this angle would be 
.
However, the question indicates that this angle lies in the 3rd quadrant. The sine of any angle in the 3rd or 4th quadrant is negative, since it is equivalent to the y-coordinate of the corresponding point on the unit circle.
Therefore,
.
The tangent of an angle yields the ratio of the opposite side to the adjacent side.
If this ratio is
However, the question indicates that this angle lies in the 3rd quadrant. The sine of any angle in the 3rd or 4th quadrant is negative, since it is equivalent to the y-coordinate of the corresponding point on the unit circle.
Therefore,
If 
, which of the following angles is NOT a possible value for 
?
If
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On the unit circle, the cosine of an angle yields the x-coordinate.
There are two angles at which the _x-_coordinate on the unit circle is 
: 
and 
.
is coterminal with 
, and 
is coterminal with 
.
is in the 4th quadrant, and has a positive x-coordinate.
On the unit circle, the cosine of an angle yields the x-coordinate.
There are two angles at which the _x-_coordinate on the unit circle is
How many degrees are in a unit circle?
How many degrees are in a unit circle?
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Step 1: Define a Unit Circle:
A unit circle is used in Trigonometry to draw and describe distinct angles. The unit circle works along with the coordinate grid.
Step 2: There are 
quadrants in the coordinate grid, each quadrant can fit 
degrees.
Step 3: Multiply how many degrees in 
quadrant by 
.. to get the full unit circle:
Step 1: Define a Unit Circle:
A unit circle is used in Trigonometry to draw and describe distinct angles. The unit circle works along with the coordinate grid.
Step 2: There are
Step 3: Multiply how many degrees in
What point corresponds to an angle of radians on the unit circle?
What point corresponds to an angle of
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The unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system. radians is equivalent to . This is a full circle plus a quarter-turn more. So, the angle corresponds to the point on the unit circle.
The unit circle is the circle of radius one centered at the origin
What point corresponds to the angle on the unit circle?
What point corresponds to the angle
Tap to see back →
The unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system. is equivalent to which corresponds to the point on the unit circle.
The unit circle is the circle of radius one centered at the origin
Give the angle between and that corresponds to the point .
Give the angle between
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The angle or corresponds to the point .
The angle
What point corresponds to the angle on the unit circle?
What point corresponds to the angle
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In order to find the point corresponds to the angle on the unit circle we can write:
In the unit circle which has the radious of we can write:
So the point corresponds to the angle on the unit circle is
In order to find the point corresponds to the angle
In the unit circle which has the radious of
So the point corresponds to the angle
What point corresponds to the angle on the unit circle?
What point corresponds to the angle
Tap to see back →
The unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system. is equivalent to which corresponds to the point on the unit circle.
The unit circle is the circle of radius one centered at the origin
What point corresponds to an angle of on the unit circle?
What point corresponds to an angle of
Tap to see back →
The unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system. is a full circle plus a more. So, the angle corresponds to the point on the unit circle.
The unit circle is the circle of radius one centered at the origin