#### Paros

##### New member
1.using the nodal points x0=0,x1=1/3 and x2=1 construct lagrange interpolation polynomial for the function f(x) =sin(π x/2). Hence evaluate f(3/4).

And
2.compute the roots of the equations x-sin18x=0.75 at x0=5 using Newton Raphson iterative formulae. Hint stop after six iterations.

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#### Subhotosh Khan

##### Super Moderator
Staff member
1.using the nodal points x0=0,x1=1/3 and x2=1 construct lagrange interpolation polynomial for the function f(x) =sin(π x/2). Hence evaluate f(3/4).

And
2.compute the roots of the equations x-sin18x=0.75 at x0=5 using Newton Raphson iterative formulae. Hint stop after six iterations.

What have you tried? Where are you exactly stuck?

#### Otis

##### Senior Member
I have been battling with these exercise ...
Good. You have some work to show us.

#### Paros

##### New member
The issue I have with number one is am nt sure of what i solved and the formulae am using to find f(3/4) not sure too..
And quetion 2 is I cant simplify fx into f prime. Please work it out let me learn..

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#### HallsofIvy

##### Elite Member
For $$\displaystyle f(x)= sin(\pi x/2)$$, $$\displaystyle f(0)= sin(0)= 0$$, $$\displaystyle f(1/3)= sin(\pi/6)= \frac{1}{2}$$, and $$\displaystyle f(1/2)= sin(\pi/4)= \frac{\sqrt{2}}{2}$$. The Lagrange Polynomial then is $$\displaystyle 0\frac{(x- \pi/6)(x- \pi/4)}{(0-\pi/6)(0- \pi/4)}+ \frac{1}{2}\frac{(x- 0)(x- \pi/4)}{(\pi/6- 0)(\pi/6- \pi/4)}+ \frac{\sqrt{2}}{2}\frac{(x-0)(x-\pi/6)}{(\pi/4- 0)(\pi/4- \pi/6)}$$.

#### Paros

##### New member
Sorry i taught its going to be in a tabular form

#### Otis

##### Senior Member
The issue I have with … quetion 2 is I cant [find the derivative] ... Please work it out let me learn.
Typing sin18x could mean sin(18)∙x or sin(18x). Below, I've guessed it's supposed to be sin(18x).

$$\;$$ Trig functions are functions, so it's best to use 'function notation' (i.e., type parentheses around inputs).

f(x) = x - sin(18x) - 0.75

We differentiate function f term by term:

The first term is x, and the derivative of x is 1

The second term is -sin(18x) -- that's a composite function, so we use the Chain Rule to get -18∙cos(18x)

The third term is a constant, and the derivative of any constant is 0

#### Subhotosh Khan

##### Super Moderator
Staff member
Sorry i taught its going to be in a tabular form
Can you show us the table that you need to use?

#### Paros

##### New member
Thanks Otis I think I now understand a little on that questions on the Newton raphson.. But the divided difference is not yet clear to me.
A table like the normal table we always draw in the forward n backward differences.