![]() ![]() The tangent ( BC) and cotangent ( ED) functions are the lengths of the line segments tangent to the unit circle from the axis to the terminal ray of angle θ. ![]() We have seen that the sine ( AF) and cosine ( OA) functions are vertical and horizontal segment lengths from a point on the unit circle to the axes. Let's take a look at the segments that are used to create the remaining trigonometric graphs.Įach of the six trig functions can be thought of as a segment length related to the unit circle, in a manner similar what was seen for sine and cosine. While our efforts will be concentrated on the "unwrapping" of the sine and cosine graphs, as shown above, it is interesting to note that the four remaining trigonometric graphs are formed in a similar manner. Remember that cosine is negative in Quadrants II and III (the x-coordinates are negative). ![]() The graph will repeat every period of 2 π. Like the sine graph, the cosine graph will " repeat", making it a periodic function. If these horizontal segments, starting at 0º, are progressing counterclockwise, are "unwrapped" along a horizontal line, the graph of the cosine function is formed. Remember that "cosine" is represented by the horizontal leg of the right triangle positioned in the unit circle as shown below. Remember that sine is negative in Quadrants III and IV (the y-coordinates are negative). Since the unit circle allows for multiple revolutions, the sine graph will " repeat ", which is referred to as being a periodic function. If these vertical segments, starting at 0º and progressing counterclockwise, are "unwrapped" along a horizontal line, the graph of the sine function is formed. Remember that "sine" is represented by the vertical leg of the right triangle positioned in the unit circle as shown below. This process of creating graphs from the unit circle is often called " unwrapping" the unit circle. The quadrants from the unit circle, when placed horizontally in numerical order, create the basisįor the trigonometric graphs. A unit circle is the source for the generation of the trigonometric function graphs. ![]()
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