Question

Calculus III QUESTION.

(a) Find the unit vectors that are parallel to the tangent line to the curve
y = 8 sin x
at the point (π/6, 4).

(b) Find the unit vectors that are perpendicular to the tangent line.

Answer 1

I don't know what I'm doing wrong I got, -1/2, (-1sqroot of3)/2 for a

Answer 2

\[y=8\sin x~~\Rightarrow~~y'=8\cos x\]
For \(x=\dfrac{\pi}{6}\), you have \(y'=8\cos\dfrac{\pi}{6}=\dfrac{8\sqrt3}{2}=4\sqrt3\).

The tangent line would then be
\[y-4=4\sqrt3\left(x-\frac{\pi}{6}\right)~~\iff~~y=4\sqrt3~x-\frac{2\sqrt3\pi}{3}+4\]
Is this what you have?

Answer 3

I found out what I did wrong. No that's not it. I got a different answer.
y′ = 8cosx, so m = 8cos(π/6) = 4√3.
with the vector ⟨1,4√3⟩

so you do the magnitude of that vector and you get 7. Then you divide the vector with the magnitude to get the unit vector, ⟨1/7,4√3/7⟩, then you also do the negative as well ⟨-1/7,-4√3/7⟩

Answer 4

Thank God I got it right. Got a 100 percent!!!

Answer 5

Nice job!

Answer 6

Thanks. Thanks for trying to help though