Find the reference number for each value of t t 9 pi t 5 p

Find the reference number for each value of t t = 9 pi t = 5 pi/4 t = 25 pi/6 t = 4

Solution

The reference value is simply the positive, first quadrant angle
obtained by adding or subtracting 2pi or multiples of 2pi to the given angle....

Since all these angles are in radian, we use 2pi here

a) 9pi
We can subtract 8pi
9pi - 8pi = pi
So, the reference value is : 0 --> ANSWER

b) -5pi/4
First add 2pi to make it positive
-5pi/4 + 2pi is 3pi/4
Now, this is in quadrant 2
So, for quadrant 2, reference value = pi - angle
RV= pi - 3pi/4
RV = pi/4 ---> ANSWER

c) 25pi/6
First subtract 4pi from this to get it to an angle within 0 to 2pi
25pi/6 - 4pi
is pi/6
This is already an angle in quadrant 1
So, reference value = pi/6 ---> ANSWER

d) t = 4
We know that t = 4 lies between pi and 3pi/2
So, this is in quadrant 3
So, for quadrant, 3 reference value = angle - pi
RV = 4 - pi
RV = 0.8584073464102068 ---> ANSWER