Question

Find the roots please

Answer 1

\[\frac{3}{4} \tan \theta- .7\sin^2 \theta+\frac{1}{2}=0\]

By Newton-Raphson Method

Answer 2

do you know the formula of newton raphson method?

Answer 3

yes

Answer 4

the function you have written, has to be diffferentiated.

so differentiate the function.
can you do that?

Answer 5

wait

Answer 6

\[f'(\theta)=\frac{3}{4}\sec^2 \theta- \frac{7}{5}\sin \theta \cos \theta\]

Answer 7

yes. absolutely correct you did.!

Answer 8

and you know the formula of newton raphson method.

it is.
\[x _{n+1} = x _{n} - \frac{ f(x) }{ f'(x) }\]

guess the value of the \[x _{n}\] and compute the value of your function and the derivative at the value you guessed.
and get the value.

keep doing this process till the answer comes out to be same.

usually, i use excel to solve questions based on iterations.

Answer 9

can you do it? now?

Answer 10

how can i guess the \[x _{n}?\]
any number?
can i say 15?

Answer 11

Ideally you want to pick a number close to the eventual root...

Answer 12

how can i know which one is close to the root?

Answer 13

Sketching a graph of the function and its derivative may give you some ideas. You're going to converge on the nearest root to the starting point you choose, I think, so if you want to get all of them, you need to have some idea of where they might be...

Answer 14

Helpful to know if your function is periodic, too!

Answer 15

yes you can take any number..
you may take numbers like 30 or 45.... for it would be easier to calculate tan(45) or sin(30)
rather than choosing number like 20 or 15.

and to find which number would be closest to the root, look at the diagram.

Answer 16

does this thing helps??