Concept

Unit Circle

The unit circle is a circle with radius

1

and whose center lies on the origin of a coordinate plane.

A right triangle can be associated to a point on the circle. This can be done by choosing its hypotenuse equal to the radius of the circle. The legs of the triangle are parallel to the axes.

The coordinates of a point on the unit circle can be related to trigonometric ratios by selecting $θ$ as the angle that is at the origin.

The length of the hypotenuse is equal to one because it is the radius of the unit circle, so the point on the unit circle can be used to generalize sine and cosine functions.

sin θ = \frac{opp}{hyp} cos θ = \frac{adj}{hyp} ⇓ sin θ = y cos θ = x

Because of this, sine and cosine are also called circular functions.

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Concept

Unit Circle

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