At what points does the curve have vertical and horizontal tangents?

Question

astrophysics · Answer

Not sure if this is an error or how you work it, but I haven't seen an example as such, ok so, 

$$x = 2\cos(t)-\cos(2t)~~~~y=2\sin(t)-\sin(2t)$$

Solution says $$x=2acost-acos2t$$ then finding the derivative of this and same with the other, but where did the a come from and why are we using it here?

ganeshie8 · Answer

a shouldn't be there in the solution

astrophysics · Answer

Ok so it definitely is an error right? I was just staring at it and was like where the heck did the a come from haha.

astrophysics · Answer

Check it: http://puu.sh/bSnXG/241e6ce2a7.png

ganeshie8 · Answer

it seems the equations in question have a typo
they forgot "a"

astrophysics · Answer

Oh ok, that makes sense, I'll just add an a :P thanks!

ganeshie8 · Answer

horizontal tangents occur at :  dy/dt = 0

vertical tangents occur at : dx/dt = 0

astrophysics · Answer

Yup

ganeshie8 · Answer

the solution looks fine to me :)

astrophysics · Answer

Thanks, for checking :p.

Hey, while you're here when you have problems finding the area of the regions that lies between first curve and outside the second curve does the basic execution of integrals still apply, such as f(x)-g(x) upper - lower?