Is csc X is discontinuous?

(i) The graph of the function y = csc x is not a continuous graph, but consists of infinite number of separate branches, the points of discontinuities are at x = nπ, where n = 0, ±1, ±2, ±3, ±4, …………… .

How do you write cosecant?

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. Since it is the reciprocal of sine, we write it as csc x = 1 / sin x.

How do you find a cosecant period?

Explanation: By definition, csc(x)=1sin(x) . Therefore, its period is the same as the period of sin(x) , that is, 2π .

What is the period of a cosecant graph?

The period of both secant and cosecant is 2π like sine and cosine. There is no amplitude for secant and cosecant, but there is a vertical stretch that is used instead.

Is csc even or odd?

Cosine and secant are even; sine, tangent, cosecant, and cotangent are odd.

What is csc?

The cosecant ( csc ⁡ ) (csc) (csc)

The cosecant is the reciprocal of the sine. It is the ratio of the hypotenuse to the side opposite a given angle in a right triangle.

What functions have period 2pi?

The sine and cosine functions both have a period of 2π radians. The cosine function is very similar to the sine, except that it is “ahead” of the sine by π / 2 radians. The sine function takes the value of zero at zero degrees, where as the cosine is 1 at the same point.

Is cosecant function continuous?

∴ cosec x is continuous at every point of domain.

What is the domain of cosecant?

The graph of the cosecant function looks like this: The domain of the function y=csc(x)=1sin(x) is all real numbers except the values where sin(x) is equal to 0 , that is, the values πn for all integers n . The range of the function is y≤−1 or y≥1 .

Does SEC and csc have amplitude?

The sine and cosine functions will have an amplitude. However, the tangent, cotangent, secant, and cosecant functions do not have an amplitude because these functions do not have a maximum value nor a minimum value.

What is the value of cosecant?

The secant of x is 1 divided by the cosine of x: sec x = 1 cos x , and the cosecant of x is defined to be 1 divided by the sine of x: csc x = 1 sin x .