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Illustration of spiral with unequally spaced intervals.

Spiral

Illustration of spiral with unequally spaced intervals.

Illustration of spiral with unequally spaced intervals.

Spiral

Illustration of spiral with unequally spaced intervals.

Illustration of spiral with unequally spaced intervals.

Spiral

Illustration of spiral with unequally spaced intervals.

Illustration of an ellipse.

Ellipse

Illustration of an ellipse.

Illustration of an ellipse.

Ellipse

Illustration of an ellipse.

Illustration of an ellipse.

Ellipse

Illustration of an ellipse.

Illustration of a stepladder that is opened to form an isosceles triangle with the ground.

Open Stepladder

Illustration of a stepladder that is opened to form an isosceles triangle with the ground.

Illustration of a giant stepladder, sometimes called a skyscraper stepladder, that is opened next to a palm tree. One of the bottom legs of the unfolded ladder is adjacent to the tree. The ladder forms an isosceles triangle with the ground.

Skyscraper Giant Stepladder

Illustration of a giant stepladder, sometimes called a skyscraper stepladder, that is opened next to…

Illustration of a stepladder that is opened to form an isosceles triangle with the ground.

Open Stepladder

Illustration of a stepladder that is opened to form an isosceles triangle with the ground.

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane. The circle is divided into four quadrants by the x- and y- axes. The circle can be labeled and used to find the six trigonometric values (sin, cos, tan, cot, sec, csc, cot) at each of the quadrantal angles.

Unit Circle

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane. The…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. The circle is marked and labeled in both radians and degrees in 45° increments. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled In 45 ° Increments

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. The circle is marked and labeled in radians. All quadrantal angles and angles that have reference angles of 30°, 45°, and 60° are given in radian measure in terms of pi. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Special Angles And Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. All quadrantal angles and angles that have reference angles of 30°, 45°, and 60° are given in radian measure in terms of pi. At each quadrantal angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled At Special Angles

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. All quadrantal angles and angles that have reference angles of 30°, 45°, and 60° are given in radian measure in terms of pi.

Unit Circle Labeled At Special Angles

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane. All quadrantal angles and angles that have reference angles of 30°, 45°, and 60° are marked from the origin, but no values are given.

Unit Circle Marked At Special Angles

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane. All…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. All quadrantal angles are given in radian measure in terms of pi.

Unit Circle Labeled At Quadrantal Angles

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane. All quadrantal angles are given in radian measure in terms of pi. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Quadrantal Angles And Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane. All…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane. At each quadrantal angle, the coordinates are given, but not the angle measure. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Quadrantal Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane. At each…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. At each quadrantal angle, the coordinates are given, but not the angle measure. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Quadrantal Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. All quadrantal angles are given in degree measure. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Quadrantal Angles And Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. All quadrantal angles are given in both radian and degree measure. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Quadrantal Angles And Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. At 45° increments, the angles are given in both radian and degree measure. At each quadrantal angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled In 45° Increments With Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. At 45° increments, the angles are given in both radian and degree measure. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled In 45° Increments With Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. The circle is marked and labeled in both radians and degrees at all quadrantal angles and angles that have reference angles of 30°, 45°, and 60°. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Special Angles And Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. The circle is marked and labeled in both radians and degrees at all quadrantal angles and angles that have reference angles of 30°, 45°, and 60°. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Special Angles And Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. At 30° increments, the angles are given in both radian and degree measure. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled In 30° Increments With Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

This diagram shows the relation of units of slope.

Slope Units

This diagram shows the relation of units of slope.

A man measuring the height of a tree by determining the angle and how far away he is standing.

Measuring Tree Height

A man measuring the height of a tree by determining the angle and how far away he is standing.

A caliper used for measuring the diameter of a circle.

Caliper

A caliper used for measuring the diameter of a circle.

Angles 1 and 2 are adjacent angles. Two angles with a common vertex and a common side between them are adjacent angles.

Adjacent Angles

Angles 1 and 2 are adjacent angles. Two angles with a common vertex and a common side between them are…

Angle 3 is an acute angle.

Acute Angle

Angle 3 is an acute angle.

Illustration of supplementary angles. Angles LMK and KMH are supplementary.

Supplementary Angles

Illustration of supplementary angles. Angles LMK and KMH are supplementary.

Illustration showing that the sum of angle 1 and angle 2 is angle ABC.

Sum of Angles

Illustration showing that the sum of angle 1 and angle 2 is angle ABC.

Illustration showing that the difference between angle 1 and angle 2 is angle ABC.

Difference of Angles

Illustration showing that the difference between angle 1 and angle 2 is angle ABC.

Illustration showing two positive angles; angle 1 being the acute angle and angle 2 being the reflex angle.

Acute and Reflex Angles

Illustration showing two positive angles; angle 1 being the acute angle and angle 2 being the reflex…

Illustration showing four angles that can be used to define different relationships, such as adjacent, supplementary, etc..

Relationships Between 4 Angles

Illustration showing four angles that can be used to define different relationships, such as adjacent,…

Illustration showing four angles that can be used to define different relationships, such as adjacent, supplementary, etc..

Relationships Between 4 Angles

Illustration showing four angles that can be used to define different relationships, such as adjacent,…

Illustration showing angles 1 and 2 are supplementary and angles ACD and DCB are supplementary. Also, Angles ACD and DCB are right angles.

Supplementary and Right Angles

Illustration showing angles 1 and 2 are supplementary and angles ACD and DCB are supplementary. Also,…

Illustration used to prove that all right angles are equal.

Equal Right Angles

Illustration used to prove that all right angles are equal.

Illustration showing that the sum of all the angles about a point equals 360°.

360° Sum of Angles

Illustration showing that the sum of all the angles about a point equals 360°.

Illustration showing that angles 1 and 2 are vertical and angles 3 and 4 are vertical.

Vertical Angles

Illustration showing that angles 1 and 2 are vertical and angles 3 and 4 are vertical.

Illustration showing that angles 1 and 2 are complementary.

Complementary Angles

Illustration showing that angles 1 and 2 are complementary.

Illustration showing that angles 1 and 2 are supplementary.

Supplementary Angles

Illustration showing that angles 1 and 2 are supplementary.

Illustration showing six angles that can be used to define different relationships, such as adjacent, supplementary, etc..

Relationships Between 6 Angles

Illustration showing six angles that can be used to define different relationships, such as adjacent,…

Illustration showing optical illusions. It is not always possible to trust the eye to be sure if the lengths of lines a and b are the same. You would need to measure to be sure of your conclusion.

Optical Illusions

Illustration showing optical illusions. It is not always possible to trust the eye to be sure if the…

Illustration showing optical illusions. It is not always possible to trust the eye to be sure if the lengths of lines a and b are the same. You would need to measure to be sure of your conclusion.

Optical Illusions

Illustration showing optical illusions. It is not always possible to trust the eye to be sure if the…

Illustration showing optical illusions. It is not always possible to trust the eye to be sure if the lengths of lines a and b are the same. You would need to measure to be sure of your conclusion.

Optical Illusions

Illustration showing optical illusions. It is not always possible to trust the eye to be sure if the…

Illustration showing optical illusions. It is not always possible to trust the eye to be sure if the lengths of lines a and b are the same. You would need to measure to be sure of your conclusion.

Optical Illusions

Illustration showing optical illusions. It is not always possible to trust the eye to be sure if the…

Illustration showing optical illusions. It is not always possible to trust the eye to be sure if the lines are the same distance apart. You may need to measure to be sure of your conclusion.

Optical Illusions

Illustration showing optical illusions. It is not always possible to trust the eye to be sure if the…

Illustration showing optical illusions. It is not always possible to trust the eye to be sure if the lines are the same distance apart. You may need to measure to be sure of your conclusion.

Optical Illusions

Illustration showing optical illusions. It is not always possible to trust the eye to be sure if the…

Illustration showing optical illusions. It is not always possible to trust the eye to be sure if the lines are prolongations of the other lines. You may need to measure to be sure of your conclusion.

Optical Illusions

Illustration showing optical illusions. It is not always possible to trust the eye to be sure if the…

Illustration showing optical illusions. It is not always possible to trust the eye to be sure if the lines are prolongations of the other lines. You may need to measure to be sure of your conclusion.

Optical Illusions

Illustration showing optical illusions. It is not always possible to trust the eye to be sure if the…

Euclid, a great mathematician, wrote the first systematic textbook on geometry.

Euclid

Euclid, a great mathematician, wrote the first systematic textbook on geometry.

Illustration showing how to construct the bisector of an angle.

Construction Of Angle Bisector

Illustration showing how to construct the bisector of an angle.

Illustration showing a circle with a radius of 2 in. intersecting a circle with a radius of 3 in..

2 Intersecting Circles

Illustration showing a circle with a radius of 2 in. intersecting a circle with a radius of 3 in..

Illustration showing a perpendicular bisector of a triangle extended outside of the triangle.

Triangle With Perpendicular Bisector

Illustration showing a perpendicular bisector of a triangle extended outside of the triangle.

Illustration of the construction used to make a perpendicular bisector of a straight line.

Construction Of A Perpendicular Bisector Of A Straight Line

Illustration of the construction used to make a perpendicular bisector of a straight line.

Illustration of the construction used to create a perpendicular to a straight line at a given point.

Construction Of A Perpendicular To A Straight Line

Illustration of the construction used to create a perpendicular to a straight line at a given point.

Illustration of the construction used to create a perpendicular to a straight line from a given point not on the line.

Construction Of A Perpendicular To A Straight Line

Illustration of the construction used to create a perpendicular to a straight line from a given point…

Illustration used to prove that "If one side of a triangle is prolonged, the exterior angle formed is greater than either of the remote interior angles."

Exterior Angle of Triangle Theorem

Illustration used to prove that "If one side of a triangle is prolonged, the exterior angle formed is…