Maths question

A pendulum 48cm long has swung through a certain angle theta,starting from the vertical,the Bob is 8cm higher than its lowest position.without use of a calculator find the bob's further gain in height when the pendulum has swung and angle 2theta from the vertical,twice as large as the first (hint:use cos2theta=2cos^2theta-1)

What I have done so far
48-8=40
48 x(2cos^2theta-1)
Expand
48x2x(40/48)^2
=2x40^2/48-48
Not sure if this is right

It's probably is right; but you really need to explain what you're doing as you go along, rather than just writing down formulae/equations. I can guess what those bits and pieces represent, but I shouldn't have to. It would also help your own understanding, if you're struggling.

E.g.

Vertical height of pendulum below suspension point when at angle theta = 48-8 = 40

So $\cos\theta = 40/48 = 5/6$

Vertical height of pendulum below suspension point when at angle $2\theta$

$=48\cos 2\theta$

$=48(2\cos^2\theta-1)$

So, yes, you're correct so far, ... and carry on.

It's probably is right; but you really need to explain what you're doing as you go along, rather than just writing down formulae/equations. I can guess what those bits and pieces represent, but I shouldn't have to. It would also help your own understanding, if you're struggling.

E.g.

Vertical height of pendulum below suspension point when at angle theta = 48-8 = 40

So $\cos\theta = 40/48 = 5/6$

Vertical height of pendulum below suspension point when at angle $2\theta$

$=48\cos 2\theta$

$=48(2\cos^2\theta-1)$

So, yes, you're correct so far, ... and carry on.

Carrying on from there I would expand the bracket so I'd have 48 x 2x (40/48)^2
=48x2x40^2/48^2-48
I'd be left with 2x40x40/48-48
I'd simplify that further
And I got 66.6 is that right and if so would that be the findal answer

In red is correct, but you've evaluated it incorrectly.

And no, it's not the final answer. Look back at my first post.

I'd subtract 48 from 66.6 =18.6
Then subtract 18.6 from 48 so the final answer would be 29.4cm
But I don't understand what I have evaluated wrong could you show me how to do it correctly ?

You'd said initially that 66.6 was your result for evaluating "2x40^2/48-48". Whereas, in fact, it was only the first part.

Also, your calculator would have shown 66.6666666, so if you're going to truncate that the three sig.fig, you want 66.7.

Finally, the question asks for the further distance risen, not the total distance; so you want to subtract your 18.7 from 40, rather than 48.

Can someone give a full answer to this question, but write it out in word format. Its hard to understand the way youve written it out.