Csc(x)
-Csc(x)Cot(x)
Csc(x) is the reciprocal of the sine function. The formal definition of the csc(x) function is:
csc(x) = 1/sin(x)
Alternatively, it can also be expressed in terms of the unit circle. For any point (x, y) on the unit circle, where the angle is measured in radians from the positive x-axis, the value of csc(x) is:
csc(x) = 1/y
The csc(x) function is undefined for values of x where sin(x) equals zero, because dividing by zero is undefined. These values occur at multiples of pi (π), where x = nπ, and n is any integer. Therefore, the domain of csc(x) is all real numbers except for nπ, where n is any integer. The range of csc(x) is from negative infinity to negative one, and from one to positive infinity.
Some common identities involving the csc(x) function are:
– csc(x) = 1/sin(x)
– sin(x) = 1/csc(x)
– csc(-x) = -csc(x)
– csc(x + nπ) = csc(x), where n is any integer.
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