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Reference Triangles on Standard Plane

Author:Dr. Doug Davis, 3D, Dr. Douglas Davis (3D)
Move the slider to change the Standard angle and see
  • a triangle with sides labeled for trigonometric functions
  • the Reference angle in each corresponding quadrant
A play button at the bottom will show the angle increasing. The right side shows the value of Sine, Cosine and Tangent as the angle is changed. A trace of the values is also shown so you can see how the functions vary. ctrl-F will clear the traces.
This is one of the main principles behind using the trigonometric functions and inverse trigonometric functions for any angle. The absolute value of the x coordinate can replace the Adjacent side and the y coordinate can replace the Opposite side of a right triangle. Adjustments can then be made for the sign of the trigonometric functions based on which quadrant the reference triangle is in. Also, shown are the values of trigonometric functions for both reference and standard angles. How do the signs of the trigonometric functions vary in the different quadrants? How would you find the inverse function of tangent in quadrant III ?

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