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This image illustrates a geometric diagram involving a circle, a triangle, and the concept of the unit circle typically used in trigonometry or geometry lessons. ### Diagram Details: - **Circle**: The large red circle is centered at the origin (0,0) of an implied Cartesian coordinate system. It represents the unit circle, which has a radius of 1. - **Horizontal and Vertical Lines**: Red lines intersect at the origin, forming the x-axis (horizontal) and y-axis (vertical). - **Triangle**: - A right triangle is formed with the circle. - The **hypotenuse** is a black line extending from the origin to a point on the circumference of the circle, marked with a red dot. - The **base** of the triangle lies along the x-axis, from the origin to where it meets the circle. - The **height** is the segment from the circumference touchpoint perpendicular to the x-axis. - **Red Dots**: The endpoints of the black hypotenuse line are marked with red dots at the origin and on the circle's circumference which highlights the vertices of the triangle. This illustration is often used to demonstrate the relationship between the sides of the triangle (base and height) with trigonometric functions such as sine and cosine on the unit circle.

This image illustrates a geometric diagram involving a circle, a triangle, and the concept of the unit circle typically used in trigonometry or geometry lessons. ### Diagram Details: - **Circle**: The large red circle is centered at the origin (0,0) of an implied Cartesian coordinate system. It represents the unit circle, which has a radius of 1. - **Horizontal and Vertical Lines**: Red lines intersect at the origin, forming the x-axis (horizontal) and y-axis (vertical). - **Triangle**: - A right triangle is formed with the circle. - The **hypotenuse** is a black line extending from the origin to a point on the circumference of the circle, marked with a red dot. - The **base** of the triangle lies along the x-axis, from the origin to where it meets the circle. - The **height** is the segment from the circumference touchpoint perpendicular to the x-axis. - **Red Dots**: The endpoints of the black hypotenuse line are marked with red dots at the origin and on the circle's circumference which highlights the vertices of the triangle. This illustration is often used to demonstrate the relationship between the sides of the triangle (base and height) with trigonometric functions such as sine and cosine on the unit circle.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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I was wondering what the formula is for finding the length of the black line in the attached image. 

This image illustrates a geometric diagram involving a circle, a triangle, and the concept of the unit circle typically used in trigonometry or geometry lessons. ### Diagram Details: - **Circle**: The large red circle is centered at the origin (0,0) of an implied Cartesian coordinate system. It represents the unit circle, which has a radius of 1. - **Horizontal and Vertical Lines**: Red lines intersect at the origin, forming the x-axis (horizontal) and y-axis (vertical). - **Triangle**: - A right triangle is formed with the circle. - The **hypotenuse** is a black line extending from the origin to a point on the circumference of the circle, marked with a red dot. - The **base** of the triangle lies along the x-axis, from the origin to where it meets the circle. - The **height** is the segment from the circumference touchpoint perpendicular to the x-axis. - **Red Dots**: The endpoints of the black hypotenuse line are marked with red dots at the origin and on the circle's circumference which highlights the vertices of the triangle. This illustration is often used to demonstrate the relationship between the sides of the triangle (base and height) with trigonometric functions such as sine and cosine on the unit circle.
Transcribed Image Text:This image illustrates a geometric diagram involving a circle, a triangle, and the concept of the unit circle typically used in trigonometry or geometry lessons. ### Diagram Details: - **Circle**: The large red circle is centered at the origin (0,0) of an implied Cartesian coordinate system. It represents the unit circle, which has a radius of 1. - **Horizontal and Vertical Lines**: Red lines intersect at the origin, forming the x-axis (horizontal) and y-axis (vertical). - **Triangle**: - A right triangle is formed with the circle. - The **hypotenuse** is a black line extending from the origin to a point on the circumference of the circle, marked with a red dot. - The **base** of the triangle lies along the x-axis, from the origin to where it meets the circle. - The **height** is the segment from the circumference touchpoint perpendicular to the x-axis. - **Red Dots**: The endpoints of the black hypotenuse line are marked with red dots at the origin and on the circle's circumference which highlights the vertices of the triangle. This illustration is often used to demonstrate the relationship between the sides of the triangle (base and height) with trigonometric functions such as sine and cosine on the unit circle.
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