arcsin

In mathematics, trigonometric functions deals with the angles and length of a triangles and also we will study different types of trigonometric functions. Let’s talk about the derivative of a function f (p) which is given by:

d / dp (f (p) ) = lim _{h →0} f (p + h) – f(p) / h.

This function is also said to be derivative or we can say differentiation with respect to ‘p’. In some cases, the differentiation of a function f (p) is known as differentiation coefficient of f (p). Now we will discuss how to find the inverse sine function or arcsin? To find this first first we will see the range and domain of arcsin function. (know more about arcsin, here)

Here the Sin^-1 p is a function and its domain value lies in between [-1, 1] and with range as [-⊼/2, ⊼/2].

Now differentiate sin^-1 p;

So we can write it as in differentiate form:

= d / dp sin^-1 p,

Let f (y) = sin^-1 y then,

F (sin⊖) = ⊖;

If we differentiate we get:

F’ (sin⊖) cos ⊖ = 1;

We can also write it as:

F’ (sin⊖) = 1 / cos⊖

Let y = sin⊖;

As we know, cos ⊖ = √ (1 – sin²âŠ–);

We know that, value of sin ⊖ is ‘y’;

So plug in value ‘y’ in place sin ⊖;

=> Cos ⊖ = √ (1 – y²);

And we know that,

= f’(sin⊖) = 1 / cos⊖

Sin ⊖ = y;

And value of cos ⊖ is √ (1 – y²);

So put the value of sin ⊖ and cos ⊖ in the given formula:

F’ (sin⊖) = 1/ cos⊖

On putting value we get:

F’ (y) = 1/√ (1 – y²),

So the differentiation of sin^-1 p is:

d / dp sin^-1 = 1 / √ (1 – p²).

This is how we can sole the inverse of arc sin function. The Constant Acceleration Equations is given by: v = v₀ + at. To get more information about acceleration then free download cbse books. It is given more systematic in cbse books and In the next session we will discuss about arctan.