The unit circle is a useful tool for understanding the basic trigonometric functions. The following functions can be defined in terms of the coordinates of points on the unit circle:
- Sine (sin): the sine of an angle is the y-coordinate of the point where the angle intersects the unit circle.
- Cosine (cos): the cosine of an angle is the x-coordinate of the point where the angle intersects the unit circle.
- Tangent (tan): the tangent of an angle is the ratio of the sine to the cosine of the angle.
- Cotangent (cot): the cotangent of an angle is the ratio of the cosine to the sine of the angle.
- Secant (sec): the secant of an angle is the reciprocal of the cosine of the angle.
- Cosecant (csc): the cosecant of an angle is the reciprocal of the sine of the angle.
Here is an image of the unit circle with these functions labeled:
In this image, the points on the circle are labeled with their coordinates (x, y), which represent the cosine and sine of the corresponding angle, respectively. The functions are labeled using their common abbreviations. For example, sin(θ) represents the sine of the angle θ, and cos(θ) represents the cosine of the angle θ. The tangent, cotangent, secant, and cosecant of θ are represented by tan(θ), cot(θ), sec(θ), and csc(θ), respectively.
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Unit Circle