Find 1 the reference number t or reference angle theta 2 the

Find (1) the reference number t or reference angle theta (2) the corresponding terminal point of each of the following t = 19 pi/3 theta = -3 pi/4 t = 23087 pi/6 and theta = 3.2

Solution

t=19pi/3

Here t lies in first quadrant and for first quadrant reference angle is the angle itself that is pi/3

terminal point (cospi/3,sinpi/3)=(1/2,sqrt3/2)

b. theta=-3pi/4

the given angle is equal to 360-3pi/4= 225 degree

point (cos 225,sin 225)= (-sqrt2/2,-sqrt2/2)

c. t= 23087pi/6

The given angle is equivakent to pi/6 which is in first quadrant. Therefore reference angle is pi/6

point (cos pi/6,sinpi/6)=(sqrt3/2,1/2)