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Explain why the range of the arc sin function is restricted to x?
Wiki User
∙ 7y ago
The range of the arcsinx function is restricted because it is the inverse of a function that is not one-to-one, a characteristic usually required for a function to have an inverse. The reason for this exception in the case of the trigonometric functions is that if you take only a piece of the function, one that repeats through the period and is able to represent the function, then an inverse is obtainable. Only a section that is one-to-one is taken and then inverted. Because of this restriction, the range of the function is limited.
Wiki User
∙ 7y ago
Wiki User
∙ 9y agoA function is normally expressed as y = f(x) where y represents the range of the function, and x refers to the domain. Consequently it is not clear what the question means.
A relationship is a function only if, for each value in the range there is at most one value in the domain which is mapped onto that value. Because of the periodicity of trigonometric functions, the range needs to be restricted. Restricting x to (-pi/2, pi/20) ensures that.
The sine function can take values in the interval [-1, 1] and so the domain, x, must be restricted to that interval because sine does not exist outside that interval.
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The integral from 0 to 2 pi of your constant value r will equal the circumference. This will be equal to 2*pi*r. This can be derived because of the following: Arc length = integral from a to b of sqrt(r^2-(dr/dtheta)^2) dtheta. By substituting the equation r = a constant c, dr/dtheta will equal 0, a will equal 0, and b will equal 2pi (the radians in a circle). By substitution, this becomes the integral from 0 to 2 pi of sqrt(c^2 + 0)dtheta, which leads us back to the original formula.
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