is arcsin an odd function The inverse of any odd function if it exists is also an odd function If f x is odd and y f x it must be that y f x Using the inverse function we can say that x f 1 y and that x f 1 y
If you ve taken any Physics or Chemistry you know that whenever any two expressions are set equal to one another they must have the same units For example F ma because the unit of force is mass times acceleration We can gain some insight as to why arcsine lacks the 1 a the same way Is arcsine an even function an odd function or neither Short Answer Expert verified The arcsine function arcsin x is an odd function Step by step solution 01 Test if arcsin x arcsin x Let s start by evaluating arcsin x We know sine function is periodic with period 2 n and sin x sin x 2 n
is arcsin an odd function
is arcsin an odd function
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In mathematics the inverse trigonometric functions occasionally also called antitrigonometric 1 cyclometric 2 or arcus functions 3 are the inverse functions of the trigonometric functions under suitably restricted domains In mathematics an even function is a real function such that for every in its domain Similarly an odd function is a function such that for every in its domain They are named for the parity of the powers of the power functions which satisfy each condition the function is even if n is an even integer and it is odd if n is an odd integer
The inverse cosine function is neither even nor odd That is the function cos 1 x cannot be computed by simply taking pm cos 1 x But it does have some symmetry given algebraically by the more complicated relation label EQU cos 1 x boxed cos 1 x pi cos 1 x nonumber Proof We kn ow that sinx is an odd function and hence its inverse sin 1x is also an odd function We can confirm this graphically graph sinx 5 5 5 5 graph arcsin x 5 5 5 5 Answer link odd Consider any odd function y g x Then taking its inverse x g 1 y x g 1 y
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Theorem Everywhere that the function is defined arcsin x arcsinx Proof Sources 1968 Murray R Spiegel Mathematical Handbook of Formulas and Tables previous next 5 Trigonometric Functions 5 80 Categories Expansion Required Proven Results Arcsine Function Examples of Odd Functions Arcsin Arcsine written as arcsin or sin 1 not to be confused with is the inverse sine function Arcsin graph The graph of y arcsin x is shown below The domain of y arcsin x is and its range is One of the properties of inverse functions is that if a point a b is on the graph of f the point b a is on the graph of its inverse
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is arcsin an odd function - In mathematics the inverse trigonometric functions occasionally also called antitrigonometric 1 cyclometric 2 or arcus functions 3 are the inverse functions of the trigonometric functions under suitably restricted domains