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Inverse Circular Functions

Consider the equation sin θ = x. This gives a unique value of x, for a given value of θ. For example, if θ = π/2 we get x = 1, if θ = 3π/2 then x = –1. But when x is given, the equation may have no solution or many (infinite) solutions. If x = 2, there is no solution since –1 ≤ sin θ ≤ 1.
To express θ as a function of x, we write θ = arc sin x or θ = sin–1 x (read as sine inverse x).
It should be noted that sin–1 x is entirely different from (sin x)–1 . The former is the measure of an angle in radians whose sine is x while the latter is 1/sin x.
We can similarly define cos–1 x as an angle in radians whose cosine is x. The other functions of this kind are tan–1 x , cot–1 x, sec–1 x , cosec–1 x. These functions are called inverse circular functions or inverse trigonometric functions.

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