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Trigonometric Functions

Functions are systematic ways to associate an element of one set with exactly one element of another set. The trigonometric functions are the basis of all trigonometry. They assign real Numbers to angle measures based on certain ratios. There are six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. Each assigns a real number to an angle measure based on a different ratio between the initial and terminal sides of the angle.

With that foundation set, well begin to learn valuable trigonometric tools: reference angles and the unit circle. Every angle that exists has a specific value for its sine, cosine, etc. But instead of having to calculate these values for every angle, we can find the value of a certain trigonometric function for the reference angle of any angle, and then use that knowledge to find the value of the trigonometric function for the given angle. Reference angles provide us with a simpler way to calculate the values of the trigonometric functions. The unit circle is a geometric figure with special relevance to the trigonometric functions. Because its radius is one, trigonometric functions are simplified when studied along the unit circle.

The sign of a trigonometric function is dependent on the signs of the coordinates of the points on the terminal side of the angle. By knowing in which quadrant the terminal side of an angle lies, you also know the signs of all the trigonometric functions. There are eight regions in which the terminal side of an angle may lie: in any of the four quadrants, or along the axes in either the positive or negative direction (the quadrantal angles). Each situation means something different for the signs of the trigonometric functions.

If f(x) = f(-x), then the function is an even function and if f(-x) = -f(x), then the function is an odd function.

Sin x, cosecx, tanx and cotx are odd functions. Cosx and sec x are even functions




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