1. double angle formula??

hi, ive been stuck on this question for days, any help would be appreciated.

a pendulum that is 48cm long has swung through an angle of x. starting from vertical it is 8cm higher than lower position. how much higher would it be after going through an angle of 2x.

we can not use a calculator (that would be slightly easy) and a hint has been given to use a cos identity. cos2x=2cos^2x-1

im not after the answer, just a point in the right direction as its been driving me insane, thanks in advance

2. Re: double angle formula??

To get started note that the height from the pendulum to the pivot is 48 cos(x), and that equals 48-8 = 40. So cos(x) = 40/48 = 5/6.

Next - for angle 2x the height from the pendulum to the pivot is 48 cos(2x). Use the cos(2x) identity and find what that is. Then subtract that from 40 to find the difference.

3. Re: double angle formula??

first of all thanks for the quick reply

so would that be cos(2x) = 2cos^2x-1
=2*(5/6)^2-1

just a bit stumped on what i subtract because that leads to a fractional answer

4. Re: double angle formula??

Yes, its a fraction: the new height is 48-48[2*(5/6)^2-1] = 29-1/3. Why does that concern you?

5. Re: double angle formula??

Sorry I confused myself, didn't realise that just needs subtracting off the initial length. Thanks for you help, makes complete sense.