question:- r=a(1-cost)
answer :- 4/3a(sin(t/2)) (which i have to prove)
Please help me to find the radius of curvature, i know the formula everything but i have to prove the answer as :- 4/3a(sin(t/2)), which i am unable to prove it,
i cannot prove the answer as above, pls help
here is the formula for finding the radius of curvature :-
radius of curvature =((r^2+(r1)^2 )^3/2)/r^2+2(r1)^2-r(r2) were
r1 is first derivative of r and
r2 is second derivative of r
Please any body help me this problem is driving me crazy,
Differentiating we get: and again we get:
Let's look at top and bottom of fraction seperately:
Using:
Again using:
So bringing them together:
Now we need to use formula:
Substituring back in our formula for curvature:
Which is the result you wanted!
Voila!
First of all thank you very much for your post
actually i know how to find derivatives, but i didnt get the idea to use half angle formula, i was stuck in that step,
but be more clear, like you posted this
Now use a "half-angle" formula: sin(t/2)= \sqrt{\frac{1}{2}(1- cos t)}
actually it made no sense like how sin(t/2)= \sqrt{\frac{1}{2}(1- cos t)}.
thanks to suhada for more clear explanation.
First of all thank you very much for your post
actually i know how to find derivatives, but i didnt get the idea to use half angle formula, i was stuck in that step,
but be more clear, like you posted this
Now use a "half-angle" formula: sin(t/2)= \sqrt{\frac{1}{2}(1- cos t)}
actually it made no sense like how sin(t/2)= \sqrt{\frac{1}{2}(1- cos t)}.
thanks to suhada for more clear explanation.