For the following values of t find a the reference number of

For the following values of t find (a) the reference number of t and (b) the terminal point determined by t.

Solution

reference number- shortest distance around the unit circle from a point on the unit circle to the x-axis terminal point- point on the unit circle that is obtained by using the counter-clockwise distance around the circle .

i) t = 7pi/3 = 2pi +pi/3

pi/3 lies in Ist quadrant so, refecernec no. is pi/3

Terminal point :( cospi/3 , sinpi/3) ---> ( 1/2 , sqrt3/2)

ii) t= -11pi/6 = - pi - 5pi/6 = -( pi +5pi/6)

It lies in IInd quadrant so, Reference no. is 5pi/6 ( distance from the -ve x axis)

Terminal Point : ( -cos5pi/6 , sin5pi/6 )= ( -sqrt3/2 , 1/2)

iii) t= 17pi/4 = 4pi +pi/4

It lies in Ist quadrant.

Reference number : pi/4

Terminal Point ( cospi/4, sinpi/4) = (1/sqrt2 , 1/sqrt2)