what is the inverse of a 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 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 0 57 sin 1 Opposite Hypotenuse sin 1 0 57 35 And now for the details 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 In general if you know the trig ratio but not the angle you can use the corresponding inverse trig function to find the angle
what is the inverse of a sine function
what is the inverse of a sine function
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The Inverse Of One to One Functions Inverse Functions General
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Question Video Recognizing The Inverse Of The Sine Function From A
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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 Because the sine function is one to one on this domain its inverse is a function The graph of the inverse sine function y sin 1 x is shown below Its domain is the same as the range of the sine function namely 1 leq x leq 1 and its range is our restricted domain for sine frac pi 2 leq y leq frac pi 2
Review your knowledge of the inverse trigonometric functions arcsin x arccos x arctan x What are the inverse trigonometric functions arcsin x or sin 1 x is the inverse of sin x 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 used in engineering navigation physics and geometry
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The inverse of sin function or sin 1 also known as arcsin or asine obtains the angle if it takes the ratio Opposite side Hypotenuse side Sine Inverse is represented by sin 1 or arcsin Sin Inverse Example In a triangle PQR PQ 4 9 cm QR 4 0 cm and PR 2 8 CM and angle Q 35 image will be uploaded soon Inverse functions in the most general sense are functions that reverse each other For example here we see that function f takes 1 to x 2 to z and 3 to y A mapping diagram The map is titled f The first oval contains the values one two and three The second oval contains the values x y and z
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 Inverse trigonometric functions are the inverse functions of the basic trigonometric functions which are sine cosine tangent cotangent secant and cosecant functions The inverse trigonometric functions are written using arc prefix like arcsin x arccos x arctan x arccsc x arcsec x arccot x
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what is the inverse of a sine function - Because the sine function is one to one on this domain its inverse is a function The graph of the inverse sine function y sin 1 x is shown below Its domain is the same as the range of the sine function namely 1 leq x leq 1 and its range is our restricted domain for sine frac pi 2 leq y leq frac pi 2