Use the iterative formula $$x_{n+1}={3 \over 4}\pi-\sin x$$to determine the root correct to 2 decimal places. Give the result of each iteration to 4 decimal places.

Question

anonymous · Answer

where's your initial guess?

anonymous · Answer

between 1.3 and 1.5

anonymous · Answer

@phi

anonymous · Answer

@apoorvk @dumbcow @experimentX @Laura* @Mani_Jha @Zarkon I know one of you will have the answer :D

phi · Answer

Get out your calculator and type in
0.75*pi - sin(1.4)
and write down the answer to four decimal places. That is x1
now do the same thing, except replace the 1.4 with x1.  You get a new number x2
write it down.
keep doing this until the numbers stop changing (to at least 3 decimal places)

phi · Answer

be sure to use radians for the sin

anonymous · Answer

Ok, that makes sense. It takes a long time though. Yes, don't worry. :D

phi · Answer

It converges very quickly

phi · Answer

Here's what you should get (but you should round your numbers to 4 places)
 1 1.400000
 2 1.370745
 3 1.376138
 4 1.375081
 5 1.375286
 6 1.375246

anonymous · Answer

Muchas gracias!