Trigonometric Functions of any angle

                  Trigonometric Functions of any angle

The trigonometric functions of any angle can be defined using the unit circle and the coordinates of a point on the circle corresponding to that angle. Let's consider an angle � in standard position (measured counter clockwise from the positive x-axis). The point where the terminal side of the angle intersects the unit circle has coordinates (cos⁡�,sin⁡�).

Here are the definitions of the main trigonometric functions for any angle �:

  1. Sine (sin⁡�): The sine of � is the y-coordinate of the point where the terminal side of � intersects the unit circle. sin⁡�=��

  2. Cosine (cos⁡�): The cosine of � is the x-coordinate of the point where the terminal side of � intersects the unit circle. cos⁡�=��

  3. Tangent (tan⁡�): The tangent of � is the ratio of the sine of � to the cosine of �. tan⁡�=sin⁡�cos⁡�

  4. Cosecant (csc⁡�): The cosecant of � is the reciprocal of the sine of �. csc⁡�=1sin⁡�

  5. Secant (sec⁡�): The secant of � is the reciprocal of the cosine of �. sec⁡�=1cos⁡�

  6. Cotangent (cot⁡�): The cotangent of � is the reciprocal of the tangent of �. cot⁡�=1tan⁡�=cos⁡�sin⁡�

These trigonometric functions are defined for any angle �, allowing us to evaluate them for angles in any quadrant of the coordinate plane.

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