- #1

sooyong94

- 173

- 2

## Homework Statement

The parametric equations of a curve are

##x=\frac{1}{2}(sint cost+ t), y=\frac{1}{2} t-\frac{1}{4} sin2t##,

##-\pi/2<t\leq0##. P is a point on the curve such that the gradient at P is 1. Find the equation of the normal at P. Hence, determine if the normal at P meets the curve again.

## Homework Equations

Parametric differentiation, chain rule

## The Attempt at a Solution

I have found ##\frac{dy}{dt}## and ##\frac{dt}{dx}##. ..Then ##\frac{dy}{dx}=\frac{1-cos 2t}{1+cos2t}##

I have also found out that when ##\frac{dy}{dx}=1##, ##t=\frac{-\pi}{4}##. Then the equation of the normal is ##y=-x-\frac{\pi}{4}##. Now I don't know how to determine if the normal at P meets the curve again...