csc(x)
-csc(x)cot(x)
The function csc(x) is the reciprocal of the sine function. It is defined as:
csc(x) = 1 / sin(x)
where x is the angle in radians.
The csc(x) function has certain properties:
1. The domain of csc(x) is the set of all real numbers except for the multiples of π, where the sine function is zero.
2. The range of csc(x) is the set of all real numbers except for zero, since the reciprocal of zero is undefined.
3. The graph of csc(x) is similar to that of the sine function, with asymptotes at the multiples of π where the sine function is zero.
4. The amplitude (or height) of the csc(x) function is undefined, since the reciprocal of zero is undefined. However, the minimum value of the csc(x) function is -1, as the maximum value of the sine function is 1.
5. The period of the csc(x) function is the same as that of the sine function, which is 2π.
6. csc(x) is an odd function. That is, csc(-x) = -csc(x) for all x.
7. Some common values of csc(x) include:
– csc(0) = undefined
– csc(π/6) = 2
– csc(π/4) = √2
– csc(π/3) = 2/√3
– csc(π/2) = 1.
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