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We can graph \(y=\csc x\) by observing the graph of the sine function because these two functions are reciprocals of one another. See Figure \(\PageIndex{2}\). The graph of sine is shown as a dashed orange wave so we can see the relationship.

Cosecant is one of the main six trigonometric functions and is abbreviated as csc x or cosec x, where x is the angle. In a right-angled triangle, cosecant is equal to the ratio of the hypotenuse and perpendicular.

f(x)=x^3 ; prove\:\tan^2(x)-\sin^2(x)=\tan^2(x)\sin^2(x) \frac{d}{dx}(\frac{3x+9}{2-x}) (\sin^2(\theta))' \sin(120) \lim _{x\to 0}(x\ln (x)) \int e^x\cos (x)dx \int_{0}^{\pi}\sin(x)dx

For any y = csc(x) y = csc (x), vertical asymptotes occur at x = nπ x = n π, where n n is an integer. Use the basic period for y = csc(x) y = c s c (x), (0,2π) (0, 2 π), to find the vertical asymptotes for y = csc(x) y = csc (x).

Set the argument in csc(x) csc (x) equal to πn π n to find where the expression is undefined. The domain is all values of x x that make the expression defined. The range is the set of all valid y y values. Use the graph to find the range. Determine the domain and range.

The cosecant function \( csc (\theta) \) is defined as \( \csc(\theta) = \dfrac{r}{y} \) , where \( r \) is the distance from O to M and is given by \( r = \sqrt{x^2+y^2} \).

Learn how to sketch the basic, unshifted cosecant graph, y=csc (x), with the easy 3 Steps to Sketch method!Step #1: Find Companion Equation & Essential InfoSt...

y = csc x. Note: The U shapes of the cosecant graph are tangent to its reciprocal function, sine, at sine's max and min locations. Secant Function: y = sec x

Use the reciprocal relationship between \(y=sin \, x\) and \(y=\csc \, x\) to draw the graph of \(y=A\csc(Bx)\). Sketch the asymptotes. Plot any two reference points and draw the graph through these points.