The Trig You Need for Calculus: Evaluation for Large and Negative Angles

It is important that you be able to set up the appropriate triangle to evaluate the trig functions for angles bigger than a right angle and for negative angles. Associated with such an angle is its reference angle, the smaller of the two angles it makes with the x-axis. Use the reference angle as one angle in a right triangle. Label the lengths of the sides of the triangle, being careful to assign negative lengths for sides that lie along the negative x-axis or sides that extend below the x-axis. Then read the values of the trig ratios from the triangle using the reference angle in place of the original angle. The examples below illustrate this for angles whose ending side lies in the II, III, and IV quadrants.

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