For most purposes the cosecant can be thought of as a function that assumes values over the entire real line. However, it is actually defined over the entire complex plane. Excepting, of course, points where the sine is zero.
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yes 1 + cot x^2 = csc x^2
The domain of the function f (x) = square root of (x - 2) plus 4 is Domain [2, ∞)
sqrt(x) Domain: {0,infinity) Range: {0,infinity) *note: the domain and range include the point zero.
The domain is what you choose it to be. You could, for example, choose the domain to be [3, 6.5] If the domain is the real numbers, the range is [-12.25, ∞).
The solution for cosec x equals 0 can be found by identifying the values of x where the cosecant function equals 0. Cosecant is the reciprocal of the sine function, so cosec x = 0 when sin x = 1/0 or sin x = undefined. This occurs at multiples of π, where the sine function crosses the x-axis. Therefore, the solutions for cosec x = 0 are x = nπ, where n is an integer.