1a Let Pxy be terminal points for t6 on the unit circle Why

1a.) Let P(x,y) be terminal points for t=/6 on the unit circle. Why does PQ=PR? Show that the coordinates of P satisfy: 2y=x² +(y-1)² ( <---all under the sqrt bar). Knowing x²+y²=1, simplify 2y=x² +(y-1)² ( <---all under the sqrt bar) to find P(x,y).

1b.) Using the results from 1a. use symmetry to find the terminal points at t=/3

Solution

terminal point determined by t = pi / 6

is given by ( sqrt 3/2 , 1/2 )

terminal points of t = pi/3 is

( 1/2 , sqrt 3 /2 )