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) ]
But we saw earlier that there are infinitely many answers, and the dotted line on the graph shows this. So yes there are infinitely many answers ... ... but imagine we type 0.5 into our calculator, press sin-1 and then get a never ending list of possible answers: So instead: a func...
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 notations is a...
The graph of the inverse of a function f(x) can be found as follows: Reflect the graph about the x-axis, then rotate it 90° counterclockwise(If we take the graph on the left to be the right-hand branch of y = x2, then the graph on the right is its inverse, y = .)...
A function ff is one-to-one if and only if every horizontal line intersects the graph of ff no more than once. Figure 2. (a) The function f(x)=x2f(x)=x2 is not one-to-one because it fails the horizontal line test. (b) The function f(x)=x3f(x)=x3 is one-to-one because...
In the article below, we discuss what it means to invert the sine function and what the graph of the sine inverse looks like. In particular, we'll explain the domain and range of sin inverse. Let's go! What is inverse sine? The inverse sine is, as its name suggests, the inverse ...
y= arcsin(x) = sin-1(x) solves the equationx= sin(y). Read: arcsin(x) as "the angle whose sine isx". When working with theinverse of a function, we learned that the inverse of a function can be formed by reflecting the graph over the identity liney = x. We also learned that...
Here also we have used the absolute value sign as the graph of sec-1x always has tangents with positive slopes and hence the derivative shouldn't be affected by the sign of x.Thus, the derivative of arcsec x (or) sec-1x (or) inverse sec x is 1/(|x|√x²-1)....
y = sin(x) | x = arcsin(y) Thus, ifyis equal to the sine ofx, thenxis equal to the arcsin ofy. Inverse Sine Graph If you graph the arcsin function for every possible value of sine, it forms an increasing curve from (-1, -π/2) to (1, π/2). ...
arcsin x = sin-1 x = yExamplearcsin 1 = sin-1 1 = π/2 rad = 90°Graph of arcsinArcsin rulesRule nameRule Sine of arcsine sin( arcsin x ) = x Arcsine of sine arcsin( sin x ) = x+2kπ, when k∈ℤ (k is integer) Arcsin of negative argument arcsin(-x) = - arcsin x...