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) ]
\sin ^{-1}(x)+\cos ^{-1}(x)=\frac{\pi}{2} \\ Inverse tangent Just as before: Form the graph we can get that tan^{-1} is odd and it has domain R and range (-\frac{\pi}{2},\frac{\pi}{2}). Now let’s differentiate y = tan^{−1}(x) with respect to x. x ...
The Inverse Trigonometric Functions, we learned that the graph of an inverse trigonometric function is the reflection of the original curve in the line y = x.The animations below demonstrate this better than words can.Things to doYou can choose any or all of the functions that we came across...
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, 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...
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 = ...
To find the domain and range of inverse trigonometric functions, switch the domain and range of the original functions. Each graph of the inverse trigonometric function is a reflection of the graph of the original function about the line y=xy=x....
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). ...
$$\begin{array}{*{20}c} {{}_{i}^{i - 1} T = \left( {\begin{array}{*{20}l} {\cos \theta_{i} } \hfill & { - \sin \theta_{i} } \hfill & 0 \hfill & {a_{i - 1} } \hfill \\ {\sin \theta_{i} \cos \alpha_{i - 1} } \hfill & {\cos \theta_{i...
The graph of the arcsin looks like a piece cut out of the graph of sine, and flipped. Thedomainof x is -1 ≤ x ≤ 1. Therangeof y is –π/2 ≤ y ≤π /2, inradians. Applications of the Arcsin Function Theinverse trigonometric functionsare important in engineering, navigation, phys...