Need Urgent Help!!

Let the Parametric curve; x = 8sin(t) y = 4Sqroot(3)Cos(t) 0

Question

Need Urgent Help!!

Let the Parametric curve; x = 8sin(t)    y = 4Sqroot(3)Cos(t)     0<t<3(pi)

Find slope of the tangent line at pt p(4,6)

tkhunny · Answer

Have you considered finding the value of t that puts you at (4,6)?  Don't forget to make sure that you get there only once.

rmrjr22 · Answer

making a chart and plugging every point in until i reach (4,6)?

tkhunny · Answer

You're not serious!

Why not solve for t in $8\sin(t) = 4$, finding all solutions in $0 < t < 3\pi$.

rmrjr22 · Answer

thats what im trying to figure out. Going blank on parametric equations

rmrjr22 · Answer

so ur saying the arcsin(1/2) = t?

rmrjr22 · Answer

then plug in t into the y equation?

tkhunny · Answer

That is not a parametric equation.  It is a simple trig equation.  You should be up to it.

$\sin(t) = \dfrac{1}{2}$

$t = \dfrac{\pi}{6},\dfrac{5\pi}{6},\dfrac{13\pi}{6},\dfrac{17\pi}{6}$

Please stop "plugging in".  We hope you will learn to call it "substitution".

tkhunny · Answer

No, do NOT use the arcsine function.  It has a range of only $-\dfrac{\pi}{2} < t < \dfrac{\pi}{2}$.  You need $0 < t < 3\pi$.  It's just trigonometry.

rmrjr22 · Answer

arent we trying to find t so we can use it and in this case would we have to find the arcsin of 1/2 to get (pi)/6?

tkhunny · Answer

If you use the arcsine function, your ONLY possible solution will be $\pi/6$.  There are three more possible solutions.  I listed them above.

tkhunny · Answer

What we just demonstrated is that x takes on the value 4 a total of four times in $0 < t < 3\pi$.  Now, we have to hope that y takes on the value 6 for at least one of those values of t.

rmrjr22 · Answer

y = 6 at (pi)/6

tkhunny · Answer

$ 6 = 4\sqrt{3}\cos(t)$

$\cos(t) = \dfrac{\sqrt{3}}{2}$

$t = \dfrac{\pi}{6}, \dfrac{11\pi}{6}, \dfrac{13\pi}{6}$

Whoops!  if you just go with $\pi/6$, you WILL MISS the other solution.

tkhunny · Answer

You must be thorough.  Don't just guess or hope that you have it because you managed to trip over something interesting.

rmrjr22 · Answer

ok, so if they give me a point. Respectfully substitute x or y and solve for t. Correct?

tkhunny · Answer

I'm a little troubled by the original problem statement.  There are TWO solutions to this problem and it asks for the slope of "the tangent line".  There are TWO such tangent lines.  You must be sure that you find ALL solutions.  I suspect, because the problem statement goes all the way to $3\pi$, that it was intended that you would find two solutions.  The problem statement is worded oddly.  You'll be one of few who finds both solutions.

rmrjr22 · Answer

ok, so it wasnt just me. I was really confused. thought there was only supposed to be one solution. Thank you