Understanding Sine, Cosine, and Tangent - Math
Card 1 of 20

What is the
?

What is the ?
Tap to reveal answer
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In the right triangle above, which of the following expressions gives the length of y?

In the right triangle above, which of the following expressions gives the length of y?
Tap to reveal answer
is defined as the ratio of the adjacent side to the hypotenuse, or in this case
. Solving for y gives the correct expression.
is defined as the ratio of the adjacent side to the hypotenuse, or in this case
. Solving for y gives the correct expression.
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If the polar coordinates of a point are
, then what are its rectangular coordinates?
If the polar coordinates of a point are , then what are its rectangular coordinates?
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The polar coordinates of a point are given as
, where r represents the distance from the point to the origin, and
represents the angle of rotation. (A negative angle of rotation denotes a clockwise rotation, while a positive angle denotes a counterclockwise rotation.)
The following formulas are used for conversion from polar coordinates to rectangular (x, y) coordinates.


In this problem, the polar coordinates of the point are
, which means that
and
. We can apply the conversion formulas to find the values of x and y.


The rectangular coordinates are
.
The answer is
.
The polar coordinates of a point are given as , where r represents the distance from the point to the origin, and
represents the angle of rotation. (A negative angle of rotation denotes a clockwise rotation, while a positive angle denotes a counterclockwise rotation.)
The following formulas are used for conversion from polar coordinates to rectangular (x, y) coordinates.
In this problem, the polar coordinates of the point are , which means that
and
. We can apply the conversion formulas to find the values of x and y.
The rectangular coordinates are .
The answer is .
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What is the cosine of
?
What is the cosine of ?
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The pattern for the side of a
triangle is
.
Since
, we can plug in our given values.


Notice that the
's cancel out.

The pattern for the side of a triangle is
.
Since , we can plug in our given values.
Notice that the 's cancel out.
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If
, what is
if
is between
and
?
If , what is
if
is between
and
?
Tap to reveal answer
Recall that
.
Therefore, we are looking for
or
.
Now, this has a reference angle of
, but it is in the third quadrant. This means that the value will be negative. The value of
is
. However, given the quadrant of our angle, it will be
.
Recall that .
Therefore, we are looking for or
.
Now, this has a reference angle of , but it is in the third quadrant. This means that the value will be negative. The value of
is
. However, given the quadrant of our angle, it will be
.
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What is the
?

What is the ?
Tap to reveal answer
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In the right triangle above, which of the following expressions gives the length of y?

In the right triangle above, which of the following expressions gives the length of y?
Tap to reveal answer
is defined as the ratio of the adjacent side to the hypotenuse, or in this case
. Solving for y gives the correct expression.
is defined as the ratio of the adjacent side to the hypotenuse, or in this case
. Solving for y gives the correct expression.
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If the polar coordinates of a point are
, then what are its rectangular coordinates?
If the polar coordinates of a point are , then what are its rectangular coordinates?
Tap to reveal answer
The polar coordinates of a point are given as
, where r represents the distance from the point to the origin, and
represents the angle of rotation. (A negative angle of rotation denotes a clockwise rotation, while a positive angle denotes a counterclockwise rotation.)
The following formulas are used for conversion from polar coordinates to rectangular (x, y) coordinates.


In this problem, the polar coordinates of the point are
, which means that
and
. We can apply the conversion formulas to find the values of x and y.


The rectangular coordinates are
.
The answer is
.
The polar coordinates of a point are given as , where r represents the distance from the point to the origin, and
represents the angle of rotation. (A negative angle of rotation denotes a clockwise rotation, while a positive angle denotes a counterclockwise rotation.)
The following formulas are used for conversion from polar coordinates to rectangular (x, y) coordinates.
In this problem, the polar coordinates of the point are , which means that
and
. We can apply the conversion formulas to find the values of x and y.
The rectangular coordinates are .
The answer is .
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What is the cosine of
?
What is the cosine of ?
Tap to reveal answer
The pattern for the side of a
triangle is
.
Since
, we can plug in our given values.


Notice that the
's cancel out.

The pattern for the side of a triangle is
.
Since , we can plug in our given values.
Notice that the 's cancel out.
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If
, what is
if
is between
and
?
If , what is
if
is between
and
?
Tap to reveal answer
Recall that
.
Therefore, we are looking for
or
.
Now, this has a reference angle of
, but it is in the third quadrant. This means that the value will be negative. The value of
is
. However, given the quadrant of our angle, it will be
.
Recall that .
Therefore, we are looking for or
.
Now, this has a reference angle of , but it is in the third quadrant. This means that the value will be negative. The value of
is
. However, given the quadrant of our angle, it will be
.
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What is the
?

What is the ?
Tap to reveal answer
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In the right triangle above, which of the following expressions gives the length of y?

In the right triangle above, which of the following expressions gives the length of y?
Tap to reveal answer
is defined as the ratio of the adjacent side to the hypotenuse, or in this case
. Solving for y gives the correct expression.
is defined as the ratio of the adjacent side to the hypotenuse, or in this case
. Solving for y gives the correct expression.
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If the polar coordinates of a point are
, then what are its rectangular coordinates?
If the polar coordinates of a point are , then what are its rectangular coordinates?
Tap to reveal answer
The polar coordinates of a point are given as
, where r represents the distance from the point to the origin, and
represents the angle of rotation. (A negative angle of rotation denotes a clockwise rotation, while a positive angle denotes a counterclockwise rotation.)
The following formulas are used for conversion from polar coordinates to rectangular (x, y) coordinates.


In this problem, the polar coordinates of the point are
, which means that
and
. We can apply the conversion formulas to find the values of x and y.


The rectangular coordinates are
.
The answer is
.
The polar coordinates of a point are given as , where r represents the distance from the point to the origin, and
represents the angle of rotation. (A negative angle of rotation denotes a clockwise rotation, while a positive angle denotes a counterclockwise rotation.)
The following formulas are used for conversion from polar coordinates to rectangular (x, y) coordinates.
In this problem, the polar coordinates of the point are , which means that
and
. We can apply the conversion formulas to find the values of x and y.
The rectangular coordinates are .
The answer is .
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What is the cosine of
?
What is the cosine of ?
Tap to reveal answer
The pattern for the side of a
triangle is
.
Since
, we can plug in our given values.


Notice that the
's cancel out.

The pattern for the side of a triangle is
.
Since , we can plug in our given values.
Notice that the 's cancel out.
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If
, what is
if
is between
and
?
If , what is
if
is between
and
?
Tap to reveal answer
Recall that
.
Therefore, we are looking for
or
.
Now, this has a reference angle of
, but it is in the third quadrant. This means that the value will be negative. The value of
is
. However, given the quadrant of our angle, it will be
.
Recall that .
Therefore, we are looking for or
.
Now, this has a reference angle of , but it is in the third quadrant. This means that the value will be negative. The value of
is
. However, given the quadrant of our angle, it will be
.
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What is the
?

What is the ?
Tap to reveal answer
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In the right triangle above, which of the following expressions gives the length of y?

In the right triangle above, which of the following expressions gives the length of y?
Tap to reveal answer
is defined as the ratio of the adjacent side to the hypotenuse, or in this case
. Solving for y gives the correct expression.
is defined as the ratio of the adjacent side to the hypotenuse, or in this case
. Solving for y gives the correct expression.
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If the polar coordinates of a point are
, then what are its rectangular coordinates?
If the polar coordinates of a point are , then what are its rectangular coordinates?
Tap to reveal answer
The polar coordinates of a point are given as
, where r represents the distance from the point to the origin, and
represents the angle of rotation. (A negative angle of rotation denotes a clockwise rotation, while a positive angle denotes a counterclockwise rotation.)
The following formulas are used for conversion from polar coordinates to rectangular (x, y) coordinates.


In this problem, the polar coordinates of the point are
, which means that
and
. We can apply the conversion formulas to find the values of x and y.


The rectangular coordinates are
.
The answer is
.
The polar coordinates of a point are given as , where r represents the distance from the point to the origin, and
represents the angle of rotation. (A negative angle of rotation denotes a clockwise rotation, while a positive angle denotes a counterclockwise rotation.)
The following formulas are used for conversion from polar coordinates to rectangular (x, y) coordinates.
In this problem, the polar coordinates of the point are , which means that
and
. We can apply the conversion formulas to find the values of x and y.
The rectangular coordinates are .
The answer is .
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What is the cosine of
?
What is the cosine of ?
Tap to reveal answer
The pattern for the side of a
triangle is
.
Since
, we can plug in our given values.


Notice that the
's cancel out.

The pattern for the side of a triangle is
.
Since , we can plug in our given values.
Notice that the 's cancel out.
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If
, what is
if
is between
and
?
If , what is
if
is between
and
?
Tap to reveal answer
Recall that
.
Therefore, we are looking for
or
.
Now, this has a reference angle of
, but it is in the third quadrant. This means that the value will be negative. The value of
is
. However, given the quadrant of our angle, it will be
.
Recall that .
Therefore, we are looking for or
.
Now, this has a reference angle of , but it is in the third quadrant. This means that the value will be negative. The value of
is
. However, given the quadrant of our angle, it will be
.
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