Trig Derivatives

[VyseV1]

Hello I have 2 questions on my homework that are bugging me to no end. The first is an implicit that goes to the tune of:

xsin2y=ycos2x

The other is a question that I have no idea how to do:

Determine all values of x, 0<x<2pi for which that tangents of y=sinx and y=cosx are parallel.

Any help would be greatly appreciated.

 

[pka]

\(\displaystyle \L
\begin{array}{l}
x\sin (2y) = y\cos (2x) \\
\sin (2y) + 2xy'\cos (2y) = y'\cos (2x) - 2y\sin (2x) \\
\end{array}\)

 

[VyseV1]

o ow thank you very much. Now i can sleep at night again

 

[galactus]

For the other problem. Find the derivatives of sin and cos. When the slopes are the same, then they're parallel.

\(\displaystyle \L\\\frac{d}{dx}[sin(x)]=cos(x)\)

\(\displaystyle \L\\\frac{d}{dx}[cos(x)]=-sin(x)\)

\(\displaystyle \L\\cos(x)+sin(x)=0\)

Solve for the values of x in the interval \(\displaystyle [0,2{\pi}]\)

There's 2 of them.

 

[VyseV1]

would said answers be 3pi/4 and 7pi/4

 

[galactus]

Why yes, yes they would.

 

[VyseV1]

Thanks a lot for the help guys, really appreciate it.