This is a free lesson from our course in Trigonometry The sine, cosine and tangent of an angle are all defined in terms of trigonometry, but they can also be expressed as functions. In this unit you'll examine these functions and their graphs, with the help of several examples regarding how to graph the tangent, cotangent, cosecant, and secant functions on the coordinate plane.To sketch the graph of tangent and cotangent function, you'll plot the graph in the interval - /2 <= x <= /2. On the graph, you'll plot the points whose coordinates can be taken from the table having values of tangent and cotangent functions for angle measure in radians as well as corresponding angle measure in degrees. (More text below video...)
Other useful lessons:
 Graphing Sinusoids Tangent of an Angle
(Continued from above) Each time you increase or decrease the value of the x-coordinates by a multiple of , the basic tangent and cotangent curve is repeated.
The graph of y = sec x consists of almost parabola like shapes, one above x- axis and one below x-axis. Since, sec x = 1/cos x, when the cosine approaches 0, the secant approaches infinity and this pattern is repeated over and over but it never cross x axis as secant never approaches 0.
Similarly, the graph of y = csc x which is equivalent to 1/ sin x, also consists of U shapes and upside down U shapes. Here you'll see, as sin x becomes 0, the value of csc x is undefined.
You'll also explore how to sketch the graph of y = cot x/2, y = tan 2x, y = sec 2x and y = csc x/2. Once you go through the instructor's explanation in the video, it'll be easy for you to understand how the above graphs of tangent, cotangent, cosecant and secant function can be sketched.
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