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16 wrz 2022 · The inverse functions for cotangent, cosecant, and secant can be determined by looking at their graphs. For example, the function \(y=\cot\;x \) is one-to-one in the interval \((0,\pi) \), where it has a range equal to the set of all real numbers.
We will plot the cosecant graph using its domain and range, explore the trigonometric identities of cosec x, its values, and properties. We will solve a few examples based on the concept of csc x to understand its applications better.
Example \(\PageIndex{1}\): Graphing a Variation of the Secant Function. Graph one period of \(f(x)=2.5\sec(0.4x)\). Solution. Step 1. Sketch a graph of the function \(f(x)=2.5\cos(0.4x)\). \(A=2.5\) so the stretching factor is \(2.5\). \(B=0.4\) so \(P=\dfrac{2\pi}{0.4}=5\pi\). The period is \(5\pi\) units. Dividing this by 4 gives \(\dfrac{5 ...
What is the arccosecant (arccsc x) function? The arccosecant function is the inverse of the cosecant function denoted by cosec -1x. It is represented in the graph as shown below. Therefore, the inverse of the cosecant function can be expressed as y = cosec-1x (arccosecant x) Domain and range of arccosecant are:
10 wrz 2024 · Inverse of Cosecant Function, y = cosec-1 (x) cosec -1 (x) is the inverse function of cosec(x). Its domain is (-∞, -1] U [1, ∞) and its range is [-π/2, 0) U (0, π/2].
26 mar 2016 · The graph of inverse cosecant covers angle measures from the first and fourth quadrants. On the right, the graph goes from the point down toward the horizontal asymptote as the x -values go to positive infinity.
For the inverse trigonometric functions of sine, tangent, cosecant, the negative of the values are translated as the negatives of the function. And for functions of cosine, secant, cotangent, the negatives of the domain are translated as the subtraction of the function from the π value.
