Suppose that the terminal point determined by t is the point

Suppose that the terminal point determined by t is the point (5/13, 12/13) on the unit circle. Find the terminal point determined by each of the following.

(a) t

(x, y) =

(b) t

(x, y) =

(c) + t

(x, y) =

(d) 2 + t

(x, y) =

Solution

a) t = ( 5/13 , 12/13)

pi - t

theta = tan^-1(12/13/5/13) = 67.38 deg

So pi -t would be 112 .62 deg

It mens pi -t woudl be inIIbd quadrant:

( -5/13, 12/13)

b) -t ;

(x , -y) = ( 5/13 , -12/13)

c) pi +t = 180 + 67.38 deg

IIIrd quadrant

pi +t would be ( -x, -y) = ( -5/13 , -12/13)

d) 2pi +t = t

So, (x, y) = ( 5/13 , 12/13)