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Unit Circle

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In this simulation, you’ll investigate trigonometry in the context of the unit circle. You’ll determine the sine, cosine, and tangent of various angles within the circle. Get started now working with the unit circle.

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Unit Circle Brochure

What is the unit circle?

The unit circle is a circle with a radius of one (1) unit.

What is trigonometry?

Trigonometry is a branch of mathematics that looks at the relationships of the sides and angles of triangles.

What is sine?

Sine is a trigonometric function that is equal to the ratio of the side opposite a given angle to the hypotenuse for a right triangle.

What is cosine?

Cosine is a trigonometric function that is equal to the ratio of the side adjacent to a given angle to the hypotenuse for a right triangle.

What is tangent?

Tangent is a trigonometric function that is equal to the ratio of the side opposite a given angle to the adjacent side for a right triangle.

How are angles measured?

Angles are measured using two major units, degrees and radians. There are 360 degrees in a circle and 2 pi (π) radians in a circle.

What is the Pythagorean Theorem?

The Pythagorean Theorem describes the relationship between the three sides of a right triangle (shown below).

							
								image of a right triangle. Side A is on the left. Side B is on the bottom and Side C is on top
The formula for the theorem is:

c2 = a2 + b2

where c = the hypotenuse, a = one side, and b = the other side

What are ordered pairs?

In the Cartesian plane, an ordered pair defines the “x” coordinate and the “y” coordinate of a given point. The notation for an ordered pair is: (x, y).

What are quadrants?

A quadrant is a region on a Cartesian plane that is described by the intersection of the “x” and “y” axes. The following figure shows the four quadrants.

							
								Quadrant I - the first quadrant is in the upper right hand corner of the coordinate plane. The x- and y-values in quadrant I are all positive (+).

Quadrant II - the second quadrant is in the upper left hand corner of the coordinate plane. The x-values in quadrant II are negative (-) and the y-values are positive (+).

Quadrant III - the third quadrant is in the bottom left hand corner of the coordinate plane. The x- and y-values in quadrant III are all negative (-).

Quadrant IV - the fourth quadrant is in the bottom right hand corner of the coordinate plane. The x-values in quadrant IV are positive (+) and the y-values are negative (-).

Walkthrough

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