Inverse sine function is the inverse of the sine function(opposite side/hypotenuse) of a right triangle. Arcsine function definition, formula, derivative, graph and solved examples at BYJU’S.
A plane rectangular coordinate system and a graph of the sine function (y equals to sin x) in an interval are provided on the glass plates. The distance from the origin of the plane rectangular coordinate system to a left side edge of the glass plates is equal to the distance from the ...
The arcsine of x is defined as the inverse sine function of x when -1≤x≤1.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 = y...
In fact, if we add up the heights of the function values in the two graphs above, we can get \pi/2 for any value of x. \sin ^{-1}(x)+\cos ^{-1}(x)=\frac{\pi}{2} \\ for any x in the interval [−1, 1]. This can be proved by calculus.(How?) But we can also...
The range of y = arcsec xIn calculus, sin−1x, tan−1x, and cos−1x are the most important inverse trigonometric functions. Nevertheless, here are the ranges that make the rest single-valued. If x is positive, then the value of the inverse function is always a first quadrant ...
INVERSE TRIGONOMETRIC FUNCTIONS：反三角函数 4.7INVERSETRIGONOMETRICFUNCTIONS ForaninversetoexistthefunctionMUSTbeone-to-one •Afunctionisone-tooneifforeveryxthereisexactlyoneyandforeveryythereisexactlyonex.•So •Ifxand/oryisraisedtoanevenpowerthentheinversedoesnotexistunlessthedomainisrestricted.•The...
In other words, the domain of the inverse function is the range of the original function, and vice versa, as summarized in Figure 1.Figure 1For example, if f(x)=sinxf(x)=sinx, then we would write f1(x)=sin−1xf1(x)=sin−1x. Be aware that sin−1xsin−1x does not...
By ILATE rule, the first function = sin-1x and the second function = 1. Then by using the formula of integration by parts:∫ sin-1x· 1 dx = sin-1x∫ dx - ∫ [d/dx (sin-1x) ∫ 1 dx] dx= sin-1x (x) - ∫ (1 / √(1 - x²)) x dx (Using the formula of ...
Sine Function:sin(30°) = 0.5 Inverse Sine:sin-1(0.5) = 30° CalculatorOn the calculator press one of the following (depending on the brand of calculator): either '2ndF sin' or 'shift sin'.On your calculator, try using sin and then sin-1 to see what happensMore Than One Angle!Inve...
Restrict the domain to the interval 0,infinity) to make it one-to-one.Now lets look at the trig functionsxyxyxyy = sin xy = cos xy = tan xxyFor the graph of y = sin x, the Domain is (-, ) the Range is -1, 1Not a 1-1 functionSo it currently does not have an inversexy...