Unit Circle
The circle of radius one centered at the origin in the xy-plane.
The unit circle is a circle with radius of 1 unit centered at the origin (0,0) on a coordinate plane. It is one of the most important concepts in trigonometry and is used to define the six standard trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) for angle measures in both radians and degrees.
On the unit circle, the x-coordinate of a point on the circle represents the cosine of the corresponding angle, while the y-coordinate represents the sine of the angle. For example, the point (cos(30°),sin(30°)) would be located at a point on the unit circle which corresponds to an angle of 30 degrees, where the x-coordinate is the cosine of that angle and the y-coordinate is the sine of that angle.
The unit circle also helps to define the relationship between the trigonometric functions. For example, the tangent of an angle can be found by dividing the sine of the angle by the cosine of the angle. Similarly, the secant of an angle is the reciprocal of the cosine of the angle, and so on.
The unit circle is an important tool for solving problems involving angles and trigonometric functions, and is a fundamental concept in mathematics, physics, and engineering.
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