What is the trig function for cosecant?

Cosecant (csc) – Trigonometry function In a right triangle, the cosecant of an angle is the length of the hypotenuse divided by the length of the opposite side. In a formula, it is abbreviated to just ‘csc’. csc. x.

How can you transform trigonometric graphs?

Changes to the amplitude, period, and midline of the basic sine and cosine graphs are called transformations . Changing the midline shifts the graph vertically, changing the amplitude stretches or compresses the graph vertically, and changing the period stretches or compresses the graph horizontally.

How do you write a cosecant function?

The cosecant function is the relationship between the hypotenuse and the opposite side in a right triangle. We know that cscθ=hypotenuseopposite side ⁡ θ = hypotenuse opposite side . The numerator always is larger than the denominator as the hypotenuse is the longest side.

What’s the formula for cosecant?

Based on the definitions, various simple relationships exist among the functions. For example, csc A = 1/sin A, sec A = 1/cos A, cot A = 1/tan A, and tan A = sin A/cos A.

What is the graph of cosecant?

The cosecant goes down to the top of the sine curve and up to the bottom of the sine curve. After using the asymptotes and reciprocal as guides to sketch the cosecant curve, you can erase those extra lines, leaving just y = csc x. The figure that follows shows what this function looks like all on its own.

How do you find the asymptotes of a cosecant graph?

The cosecant graph has vertical asymptotes at each value of x where the sine graph crosses the x -axis; we show these in the graph below with dashed vertical lines. Note that, since sine is an odd function, the cosecant function is also an odd function. That is, csc(− x) = − cscx.

What does each letter of the cosecant transformation function correspond to?

Considering the general form of the cosecant transformation function , what does each letter, (A, B, C, and D) correspond to? Since cosecant is a reciprocal of sine, it uses the same general formula of the sine function with the letters corresponding to the same transformations.

What is the amplitude of cosecant function?

Since cosecant is a reciprocal of sine, it uses the same general formula of the sine function with the letters corresponding to the same transformations. Note that while A does correspond to amplitude, the cosecant function extends infinitely upwards and downwards so there is no amplitude for the graphs.

What is the domain of cosecant graph?

The graph of cosecant, which is shown in Figure 2.2.2, is similar to the graph of secant. The stretching factor is | A |. The period is 2π | B |. The domain is x ≠ π | B | k, where k is an integer. The range is ( − ∞, − | A |] ∪ [ | A |, ∞). The asymptotes occur at x = π | B | k, where k is an integer.