Stu

Aha, spot on. That would be what Im looking for. Thanks. 

It was mentioned earlier but i didn't understand why or see why. I get it now, a part of the product rule, and totally overlooked. Cheers.

Why is this in radians and not degrees? It is not specified so I assume it is degree standard. Also, I do not understand how you take the /3 out side the bracked and devide the 5 to get the same result as having it inside. Also, why is it + when there is 3 - sign in the equation. I was told that the two intial minu make positive but then the - on the degree to the cos (-3) comes out side to make the + and - a negative. As shown in my example. SOme further explaination would assist me. As well, this is not the equation from last night.

in radian my answer is 4.54 regularly. There is something i have missed.

we are asked to find the 1st solution only with the guess 4.005rad and the answer to get is 5.166rad. Although my maths isn't getting that answer i believe it is going wrong somewhere in solving the formula. The anser is 5.166 because i got this once. But im not getting it every time. I do not need to solve more degrees of accuracy to get the 5.166 radian answer. It is the answer for the x0 + 1= 1 
As seen in alans answer his first solution is 5.166 although mine is not this answer. I am trying only to find where is my mistake, or have the way to input it, and way the equation final step should look, / identify my mistake to get the right answer.) 

I tried again this morning -  I got the answer 4.6877..... But it is wrong. Where is my mistake this time. That was in radians on wolfram alpha.

I believe m last answer was right in radians, though i forgot it initially and had that in degrees. If it is right what does the comment mean, "Also you should have a 4.005 multiplying the sin term in the denominator (for the first iteration only, of course." So was my answer not the correct form?

I tried again from the start. I stil lcan't get it and don't know what i need to do different/ what im doing wrong. I took the derivative/product rule or all  value. What's missing?

I found my error in the 1/x when i made it lnx. I have reworked it to make -(1/x) = derivative: 1/x^2 which should be right. I hope. Is that the only error I made?

I want to solve it, with 4.005rad to get the answer 5.166 rad. But my answer was wrong. I dont undestand your meanings, of putting the 5.266 into the question. How did you get it. Is that the second step of the formula or just proof?

yeh we got that. I think. But I think what as happening is no one was putting in the fraction answer. lol not sure how you got that.