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.
First we'll discuss functions in general and then define the six trigonometric functions. Next, we'll study the values of the trigonometric functions in the different quadrants of the coordinate plane. In each quadrant, certain functions have positive values and others have negative values.
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, 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.