When the sine of y is equal to x:sin y = xThen the arcsine of x is equal to the inverse sine function of x, which is equal to y:arcsin x = sin-1 x = yExamplearcsin 1 = sin-1 1 = π/2 rad = 90°Graph of arcsin
Inverse sine The graph of y=sin(x): The horizontal test fails. We need to restrict the domain to get the inverse function. (How about other parts?) Then it satisfies the horizontal line test, so it has an inverse f−1—sin−1(x) or arcsin(x). (Beware: the first of these not...
Inverse sine is one of the inverse trigonometric functions of the sine function and it is written as sin-1x and is read as "sin inverse x". Then by the definition of inverse sine, θ = sin-1[ (opposite side) / (hypotenuse) ]
Here we have the function f(x) = 2x+3, written as a flow diagram:The Inverse Function goes the other way:So the inverse of: 2x+3 is: (y−3)/2The inverse is usually shown by putting a little "-1" after the function name, like this:f-1(y)...
By doing so, we define the inverse sine function on the domain [−1,1][−1,1] such that for any xx in the interval [−1,1][−1,1], the inverse sine function tells us which angle θθ in the interval [−π2,π2][−π2,π2] satisfies sinθ=xsinθ=x. ...
Here is Sine and Inverse Sine plotted on the same graph: Sine and Inverse Sine They are mirror images (about the diagonal). Tilt your head to see it better. But why does Inverse Sine get chopped off at top and bottom (the dots are not really part of the function) ... ? Because ...
INVERSE TRIGONOMETRIC FUNCTIONS：反三角函数 4.7INVERSETRIGONOMETRICFUNCTIONS ForaninversetoexistthefunctionMUSTbeone-to-one •Afunctionisone-tooneifforeveryxthereisexactlyoneyandforeveryythereisexactlyonex.•So •Ifxand/oryisraisedtoanevenpowerthentheinversedoesnotexistunlessthedomainisrestricted.•The...
Inverse Trigonometric Functions In order for a trigonometric function to have an inverse, the function MUST have a restricted domain. For example: the inverse sine function is written as y = sin-1x. If we restrict the curve y = sin x to a monotonic increasing curve, it will have domain ...
Look at the sine function (inred) at the right. If we reflect this function over the identity line,y = x, we will create the inverse graph (inblue). Unfortunately, this newly formed inverse graph is not a function. Notice how the green vertical line intersects the new inverse graph in...
Inverse Trig FunctionDerivativeIntegral arcsin x1/√1-x²x arcsin x + √1-x²+ C arccos x-1/√1-x²x arccos x - √1-x²+ C arctan x1/(1+x²)x arctan x - (1/2) ln |x2+1| + C arccsc x-1/(|x|√x²-1)x arccsc x + ln |x + √x²-1| + C ...