Question

find all points on r=2sinθ where the tangent line is parallel to the ray θ=π/4

Answer 1

First to find tangent line of a function, you need the slope so we have to differentiate
dr/dtheta = 2cos(theta)
this has to be parallel to ray theta=pi/4 which is a straight line with slope of 1
set our slope equal to 1
2cos(theta) = 1
cos(theta) = 1/2
theta = arccos(1/2) = pi/3, 5pi/3

Answer 2

Answers are : (2sinπ /8,π /8),(2sin5π /8,5π /8)

Answer 3

if that helps

Answer 4

im sorry looks like i misunderstood the question
what do they mean by ray of theta=pi/4 ?

Answer 5

thanks

Answer 6

thanks for correcting me i forgot to change back to rectangular coordinates