Question

y=(sin t)/(1+cos t) , t=Π/3
equation for tangent line

Answer 1

First find the derivative..\[f \prime(x) = \frac{1}{1+ \cos(t)}\] To find the slope put pi/3 into the derivative which will be \[\frac{1}{1 + \cos(\frac{\pi}{3})}\] which is \[\frac{1}{1 + \frac{1}{2}}\] That equals 2/3.. So use the point slope formula and you should have the equation.

Answer 2

y=2/3x + pi/3?

Answer 3

plug in pi/3 into the original curve to get the corresponding y value so it will give you a point of (pi/3,y) and a slope of 2/3 and then use point slope formula

Answer 4

i got the point \[(\frac{\pi}{3},\frac{\sqrt{3}}{3})\]

Answer 5

so do \[y - \frac{\sqrt{3}}{3} = \frac{2}{3} (x - \frac{\pi}{3})\] Then solve for y

Answer 6

thank you

Answer 7

I got \[y = \frac{2}{3}x - \frac{2\pi + \sqrt{3}}{3}\]