What is the inverse of sin?

Answer 1

Inverse of sine is cosec.

Answer 2

first consider the function:

y = x^2

suppose we want to find the inverse of this function. we let y become x and x become y so we have:

x = y^2

now solve for y:

y = sqrt(x)

so, the inverse of x^2 is sqrt(x)

one thing an inverse function tells us is where it the answer came from. continuing with the present example, suppose we had the answer 144 and we wanted to know how we got this answer. we'd literally use the inverse function and find x = 12 (or -12).

so too do the trig functions have inverses (although not as easy to see as polynomials). the inverse of sin(x) is called arcsin(x) usually denoted sin^-1(x). Be careful, this does not mean 1/sin(x).

so, suppose we had sin(x) = 1/2 and we wanted to know what angle this was, we'd take the arcsin of both sides. just like the polynomials, if a function acts on its inverse they cancel and return just the argument, that is sqrt(x^2) = x (for the most part)

so:

arcsin{ sin(x) } = arcsin(1/2)

x = arcsin(1/2)
or denoted usually as:

x = sin^-1(1/2)

in my example x = 30 degrees

Answer 3

The inverse of the sine is the cosecent. Hypotenuse/Opposite
The inverse of the cosine is the secent. Hypotenuse/Adjacent
The inverse of the tangent is the cotangent. Adjacent/Opposite

Answer 4

sin = opposite/hypotenuse

this is what sin is
http://www.math10.com/en/geometry/sin-cos-tan-cot.html

this will help u too
http://library.thinkquest.org/20991/geo/stri.html


http://www.ies.co.jp/math/java/samples/asinbcos.gif
The figure shows the idea of constructing the function; y = a sin x + b cos x

The angle OAP is always 90 degrees. When the figure OAP rotates arround the origin, the y-coordinate of point P represents the function.

Answer 5

I inverse of sin is cosine or cosec

Answer 6

sin^-1 (Sine to the negative first power)

Answer 7

the inversion of SIN is SIN^-1. when talking about functions, however, COS is the inversion of SIN, COT is the inversion of TAN, and CSC is the inversion of SEC.

SIN θ = COS(pi/2 - θ)
COS θ = SIN(pi/2 - θ)
TAN θ = 1/COT θ = SIN θ/COS θ = COT(pi/2 - θ)
COT θ = 1/TAN θ = COS θ/SIN θ = TAN(pi/2 - θ)
SEC θ = 1/COS θ = CSC(pi/2 - θ)
CSC θ = 1/SIN θ = SEC(pi/2 - θ)

i've attached a link to Wikipedia that helped me immensely last year when i had to suffer through trigonometry...

Answer 8

no sure
sin^-1

Answer 9

Grace, and/or goodness.

Answer 10

csc