Unit Circle Trigonometry
This figure illustrates the geometry of the trigonometric functions on the unit circle. Note, although the figure is cropped to show the right quadrant of the unit circle, the lengths of the inscribed right-triangle correspond to the output of the trigonometric functions for any point along the unit circle.
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Sine Function The output of sine corresponds to the distance from a point on the perimeter of the unit circle to the -axis. |
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Cosine Function The output of cosine corresponds to the distance from a point on the perimeter of the unit circle to the -axis. |
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Tangent Function The output of tangent corresponds to the length of the line tangent to a point on the unit circle starting from the point and intersecting with the x-axis. |
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Cotangent Function The output of cotangent corresponds to the length of the line tangent to a point on the unit circle starting from the point and intersecting with the y-axis. |
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There are six trigonometric functions that relate to the geometry of the right-triangle sine, cosine, tangent, cosecant, secant, and cotangent. The functions take the angle of a right triangle as input and return a ratio of two of its sides.
The unit circle is a circle of radius one placed at the origin of the coordinate system. This article discusses how the unit circle represents the output of the trigonometric functions for all real numbers.
The sine function returns the sine of a number provided in radians. In geometric terms, the function returns the vertical component of the point formed by the angle on the unit circle.
The cosine function returns the cosine of an angle provided in radians. In geometric terms, the function returns the ratio of the right-triangle's adjacent side over its hypotenuse.
Given the angle of a right triangle as input returns the ratio of the triangle's opposite side over its adjacent side.
Given the angle of a right triangle as input, returns the ratio of the adjacent side over the opposite side.