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we discuss the four other trigonometric functions: tangent, cotangent, secant, and cosecant. Each of these functions are derived in some way from sine and cosine. The tangent of x is defined to be its sine divided by its cosine: tanx = sinx cosx: The cotangent of x is defined to be the cosine of x divided by the sine of x: cotx = cosx sinx:
Review all six trigonometric ratios: sine, cosine, tangent, cotangent, secant, & cosecant.
Learn how cosecant, secant, and cotangent are the reciprocals of the basic trig ratios: sine, cosine, and tangent.
Opposite. Sine, Cosine and Tangent. 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.
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)`
The graph of cotangent can be found using identical logic as tangent. You know \(\cot x=\dfrac{1}{\tan x}\). This means that the graph of cotangent will have zeros wherever tangent has asymptotes and asymptotes wherever tangent has zeroes. You also know that where tangent is 1, cotangent is also 1. Thus the graph of cotangent is:
Jan 1, 2024 · Sine (sin) and cosine (cos) are used to define all the remaining trigonometric functions: tangent (tan), cotangent (cot), secant (sec) and cosecant (csc). Their definitions are: tan = sin/cos; cot = cos/sin; sec = 1/cos; csc = 1/sin.
