What is the slope of the tangent line to the polar curve given by f(θ)= cos 2θ at the point where θ= π/6 ?

Question

these were the possible solutions to choose from....


a. -3^1/2

b. (3^1/2)/7

c. (3^1/2)/5

d. 3^1/2

e. 5(3^1/2)/3

or none of these?

Answer 1

The curve is like f(t) = cos(2t).
df/dt = -2sin(2t)

At t = π/6, df/dt = -2sin(2*π/6) = -2sin(π/3) = -2(√3/2) = -√3

So (a) is correct.

Answer 2

For ease let´s call theta =t
r=cos 2t
m= (r+tan t *dr/dt)/(-r tan t +dr/dt)
In this case
at t=pi/6
r=cospi/3=1/2
tan t= sqrt3/3
dr/dt= -2sin2t =-sqrt3
put this nimbers in the formula and you get
m=(sqrt3)/7=(b)

Answer 3

scrappy doo, the answer is definately, scrappy doo.