Consider the following. t= 31𝜋/6

Question

Consider the following.

t= 31𝜋/6

(a) Find the reference number t for the value of t.

t =

(b) Find the terminal point determined by t.

(x, y) =

Answer 1

31pi/6 - 4pi/6 = (31pi-24pi)/6= 7pi/6

7pi/6- pi

=pi6= the reference angle= the positive acute angle formed with the x axis

on a unit circle the terminal point is (x,y) = (-1/2,-(sqr3)/2)

= (-.5,-.5sqr3)

in quadrant III where all x,y coordinates are negative

= about (-.5,-.866)