Unit Circle- Understanding Its Significance in Math - Gooroo Blog (2023)

If you’re studying or preparing for trigonometry, you’ll need to know the unit circle. This circle serves as an essential tool used to solve angular sines, cosine, and tangents, ultimately the lengths of triangles. How do they work, and what information is required to use it? This article describes the unit circle and its usage in more detail.

What is a Unit Circle?

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A unit circle is typically drawn around the origin (0,0) of a X,Y axes with a radius of 1. For a straight line drawn from the circle’s centre point to a point along the circle’s edge, the length of that line is always 1. This also means that the circle’s diameter is equal to 2 because the diameter is equal to twice the length of the radius. Usually, the unit circle’s centre point is the point where the x-axis and y-axis intersect, or at the coordinates (0,0).

This is a triangulation concept that allows mathematicians to extend sine, cosine, and tangent by frequency outside the traditional right triangle. As you remember, sine, cosine, and tangent are the ratio of the sides of a triangle to a given angle, commonly referred to as theta.

Sine = the ratio of the length of the opposite side of the right triangle to the hypotenuse.
Cosine = the ratio of the length of the adjacent leg of the right triangle to the hypotenuse’s length.
Tangent = the ratio of the length of the opposite leg to the length of the adjacent leg.
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Use these traditional definitions to limit the description of angles in the right triangle from 0 to 90 degrees. In some cases, you need to know these values ​​for angles greater than 90, and the unit circle makes that possible.

These are named so because they have a radius of one unit. Its center is at the origin, and all points around the circle are one unit away from the centre. If you draw a line from the centre to a point on the circumference, the line’s length will be 1. You can then add a line to create a right triangle. This triangle will have a height equal to the y coordinate and whose length is similar to the x coordinate.

Understanding Its Use

As mentioned above, the unit circle allows you to quickly solve any order or radian sine, cosine, or tangent. Knowing the graph of the circle is especially useful if you need to solve a particular trigger value.

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Here are some tips to memorize. These tips make it easy to use for math problems that require a unit circle.

Memorize common angles and coordinates: To use the unit circle effectively, you need to remember the most common angles (both degrees and radians) and their corresponding x and y coordinates.

Find out what is negative and positive.

To find the correct value for the trigger problem, it is important to distinguish between positive and negative x and y coordinates.

How to Solve Tangent

Finally, it is essential to know how to use all this information about triangulation circles, sines and cosines to solve the tangents of angles.

Above all, review our math resources and others for additional help on this useful trigonometric tool.

About the Author

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Sam Kahn

Sam is a content creator and SEO specialist at Gooroo, a tutoring membership and online learning platform that matches students to tutors perfect for them based on their unique learning needs. Gooroo offers Math, English, SAT, Coding, Spanish tutoring, and more.


What is the significance of the unit circle? ›

A unit circle is a circle on the Cartesian Plane that has a radius of 1 unit and is centered at the origin (0, 0). The unit circle is a powerful tool that provides us with easier reference when we work with trigonometric functions and angle measurements. You can apply the Pythagorean Theorem to the unit circle.

How do you answer a unit circle? ›

The unit circle is a circle having a radius value of 1 and its center at the origin of a rectangular coordinate system. For example, if u and v are the variables in a rectangular coordinate system, the equation of the unit circle would be given by u2 + v2 = 1, and the graph of the circle would be as shown below.

What is a unit circle for dummies? ›

The unit circle is a circle with its center at the origin of the coordinate plane and with a radius of 1 unit. Any circle with its center at the origin has the equation x2 + y2 = r2, where r is the radius of the circle. In the case of a unit circle, the equation is x2 + y2 = 1.

What is the conclusion for unit circle? ›

The conclusion is that, since (−x1, y1) is the same as (cos(π − t), sin(π − t)) and (x1,y1) is the same as (cos(t),sin(t)), it is true that sin(t) = sin(π − t) and −cos(t) = cos(π − t). It may be inferred in a similar manner that tan(π − t) = −tan(t), since tan(t) = y1x1 and tan(π − t) = y1−x1.

What is the significance of the circumference of a circle? ›

The meaning of circumference is the distance around a circle or any curved geometrical shape. It is the one-dimensional linear measurement of the boundary across any two-dimensional circular surface.

What is the unit circle all formula? ›

The unit circle is the circle of radius 1 that is centered at the origin. The equation of the unit circle is x2+y2=1. It is important because we will use this as a tool to model periodic phenomena.

Is the unit circle easy? ›

The "Unit Circle" is a circle with a radius of 1. Being so simple, it is a great way to learn and talk about lengths and angles. The center is put on a graph where the x axis and y axis cross, so we get this neat arrangement here.

Is unit circle always 1? ›

"Unit" means 1, "unit circle" means circle of radius 1. A unit circle by definition has radius 1. That's what unit circle means.

Is memorizing the unit circle hard? ›

Memorizing the unit circle is actually much easier than you'd think, thanks to a couple little tricks: Trick 1: Because of the following 4 equations, we only need to memorize the unit circle values for sine and cosine. With these 4 equations, we don't even need to memorize the unit circle with tangent!

Should students memorize the unit circle? ›

You can teach the unit circle so that students don't have to memorize AND they develop a conceptual understanding of the unit circle. Students will be able to reason their way through identifying all the angles and coordinates BEFORE they ever see a completed unit circle.

What is a fact about unit circle? ›

A unit circle is a circle of unit radius with center at origin. A circle is a closed geometric figure such that all the points on its boundary are at equal distance from its center. For a unit circle, this distance is 1 unit, or the radius is 1 unit.

What are the 4 parts of the unit circle? ›

The four quadrants on the unit circle are created by dividing a 360 degree circle into 4 equal 90 degree parts. The quadrants go from 0-90, 90-180, 180-270 and 270-360.

Why was the unit circle created? ›

The unit circle was created to express these relationships for specific triangles. The term "trigonometry" was derived from the Greek "trigonometria", meaning "triangle measuring." A Greek mathematician named Hipparchus is considered to be the founder of trigonometry.

What are the special values of the unit circle? ›

Special angles are those found on the unit circle. Special angles are at 0 degrees, 30 degrees, 45 degrees, 60 degrees, and 90 degrees.

What is a fun fact about the unit circle? ›

Facts! The Unit Circle has a radius of 1. Where the center of the circle is the origin on a graph. The unit circle and trigonometry date back to the 2nd millennium BC to Egyptian mathematics and Babylonian mathematics.


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