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The trigonometric functions most widely used in modern mathematics are the sine, the cosine, and the tangent functions. Their reciprocals are respectively the cosecant, the secant, and the cotangent functions, which are less used.
In this section, we will explore the graphs of the tangent and cotangent functions. Analyzing the Graph of \(y =\tan x\) We will begin with the graph of the tangent function, plotting points as we did for the sine and cosine functions.
The three main functions in trigonometry are Sine, Cosine and Tangent. They are just the length of one side divided by another. For a right triangle with an angle θ : Sine Function: sin (θ) = Opposite / Hypotenuse. Cosine Function: cos (θ) = Adjacent / Hypotenuse. Tangent Function: tan (θ) = Opposite / Adjacent.
The tangent and cotangent graphs satisfy the following properties: range: \((-\infty, \infty)\) period: \(\pi\) both are odd functions. From the graphs of the tangent and cotangent functions, we see that the period of tangent and cotangent are both \(\pi\).
There are six trigonometric functions: sine, cosine, tangent and their reciprocals cosecant, secant, and cotangent, respectively. Sine, cosine, and tangent are the most widely used trigonometric functions.
The six trigonometric functions sine , cosine , tangent , cotangent , cosecant , and secant are well known and among the most frequently used elementary functions.
For certain values of x, the tangent, cotangent, secant and cosecant curves are not defined, and so there is a gap in the curve. [For more on this topic, go to Continuous and Discontinuous Functions in an earlier chapter.] Recall from Trigonometric Functions, that `tan x` is defined as: `tan x= (sin x)/ (cos x)`
