TUC-3+Evaluating+Trig+Functions+of+Any+Angle

This section teaches you how to solve for all 6 trigonometric functions of an angle with given information. It is important to know what is positive and negative in each Quadrant:
 * TUC-3: Evaluating Trigonometric Functions of Any Angle**

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QI: all ratios are positive QII: cos and tan are negative; sin is positive QIII: sin and cos are negative; tan is positive QIV: sin and tan are negative; cos is positive It is also important to remember the Unit Circle: The Unit Circle is needed for //__quadrantal angles__//, which are angles that land on the x or y axis. For example:

It's also important to know that the angle theta is in relation to the x-axis, and to know the ratios of each trigonometric function: Theta prime is the //__reference angle__//, which is the positive acute angle that's formed by the terminal side of the angle and the x-axis. For example, the reference angle for 47 degrees is 47 degrees. But the reference angle for 526 degrees is 14 degrees, because the ray completes one full circle (360 degrees), then has 166 degrees left to travel, but since it ends in the second quadrant, it has to be subtracted from 180 degrees. QI: reference angle = theta QII: reference angle = 180 or Pi - theta QIII: reference angle = theta - 180 or Pi QIV: reference angle = 360 or 2Pi - theta In some cases, the reference angle will need to be found first in order to find the answer to the function. If the angle involves numerous full circles, the reference angle would be the angle you'd need to next complete a circle/half circle.





Refer to these websites for extra help: http://www.mathamazement.com/Lessons/Pre-Calculus/04_Trigonometric-Functions/trigonometric-functions-of-any-angle.html http://www.themathpage.com/atrig/functions-angle.htm