inverse of the sine function

inverse of the sine function The inverse sine function is the inverse of the sine function and thus it is one of the inverse trigonometric functions It is also known as arcsin function which is pronounced as arc sin It is mathematically written as asin x or sin 1 x or arcsin x We read sin 1 x as sin inverse of x

The sine function sin takes angle and gives the ratio opposite hypotenuse The inverse sine function sin 1 takes the ratio opposite hypotenuse and gives angle And cosine and tangent follow a similar idea Example lengths are only to one decimal place sin 35 Opposite Hypotenuse 2 8 4 9 Inverse sine sin 1 does the opposite of the sine Inverse cosine cos 1 does the opposite of the cosine Inverse tangent tan 1 does the opposite of the tangent

inverse of the sine function

inverse of the sine function
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Specifically they are the inverses of the sine cosine tangent cotangent secant and cosecant functions and are used to obtain an angle from any of the angle s trigonometric ratios Inverse trigonometric functions are widely The inverse sine function sin 1 x is also called the arcsine function and denoted by arcsin x This terminology reminds us that the output of the inverse sine function is an angle or the arc on a unit circle determined by that angle as shown below

The inverse sine function is one of the inverse trigonometric functions which determines the inverse of the sine function and is denoted as sin 1 or Arcsine For example If the value of sine 90 degree is 1 then the value of inverse sin 1 or sin 1 1 will be equal to 90 This means that all the possible outputs of the sine function are between 1 and 1 in other words the range is between 1 and 1 Now if you take the inverse function arcsin the original possible outputs become the possible inputs of this inverse function

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MathWorld The inverse sine is the multivalued function sin 1 z Zwillinger 1995 p 465 also denoted arcsinz Abramowitz and Stegun 1972 p 79 Harris and Stocker 1998 p 307 Jeffrey 2000 p 124 that is the inverse function of the sine The variants Arcsinz e g Bronshtein and Semendyayev 1997 p The inverse function reverses this operation taking the ratio of sides as input and returning the angle as output begin align sin 1 left frac b c right theta cos 1 left frac a c right theta tan 1 left frac b a right theta end align

To solve for we must first take the arcsine or inverse sine of both sides The arcsine function is the inverse of the sine function 2 arcsin 2 3 1 2 arcsin 2 3 This is just one practical example of using an inverse function There are many more The inverse sine function y sin 1 x means x sin space y The inverse sine function is sometimes called the arcsine function and notated arcsin space x y sin 1 x has domain 1 1 and range left frac pi 2 frac pi 2 right

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inverse of the sine function - The inverse sine is as its name suggests the inverse of the sine function That is inverse sine finds the angle that produces a particular value of sine The common notation of this function is arcsin arcsin x y if and only if x sin y where x 1 1