Question

Help me with the algebra in this
http://i.imgur.com/avF62lx.png

I set the derivatives equal to each other, but how do I get t out of two separate trig functions?

Answer 1

set both the velocities equal to each other and solve \(t\) :
\[x'(t) = y'(t)\]

Answer 2

\[-6\pi \sin(\pi t) = 2\pi \cos(\pi t)\]

solve \(t\)

Answer 3

\[-3\sin(\pi t)=\cos(\pi t)\] I can take the arc cos of both sides but i'm still left with a variable inside of sin

Answer 4

calculator exercise i guess

Answer 5

\[-3\tan(\pi t)=1\\
\tan(\pi t)=-\frac{1}{3}\]\[\pi t=\arctan(-\frac{1}{3})\]