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) ]
give one answer when we ask "what is sin-1(x)?" 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 nev...
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 ...
Here, we have written the absolute value sign around x instead of just writing x because if we observe the graph of csc-1x, the slope of the tangent of this curve is always negative. So the derivative of csc-1x must be always negative irrespective of the sign of x. That is why we...
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). ...
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...
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...
arcsin 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 Complementary angles arcsin x = ...
The graph of an inverse functionHERE IS the definition of functions being inverses:Functions f(x and g(x) are inverses of one another, means: f(g(x)) = x and g(f(x)) = x, for all values of x in their respective domains.
{eq}\sin^{-1}(x) {/eq} or {eq}\arcsin(x) {/eq}. However, since using the symbol -1 as an exponent means to take the reciprocal in certain situations, the rest of this lesson will choose to use the notation {eq}\arcsin(x) {/eq} when referring to the inverse of the sine ...