How do you find one positive and one negative angle coterminal with 9(pi)/4?

Question

I've added and subtracted 2(pi) but I'm confused on why when I do the negative angle I need to minus 4(pi) instead of 2(pi). 

Plus in the back of my textbook, the answers say suggested answers are pi/4 and -7pi/4. Does this mean thereis multiple answers for this question?

Answer 1

"Does this mean there [are] multiple answers for this question?"

 

Yes.

 

There are an infinite number of positive (CCW) and negative (CW) angles for every terminal ray. They differ in value by n rotations, n integer. All of them have the same trig function values.

 

1 rotation = 360° = 2 pi radians.

Answer 2

Draw a sketch of the four quadrants. The line to the right is 0 degrees or 360 degrees ( 0 pi or 2 pi radians). The line straight up is 90 degrees ( 1/2 pi radians) the line to the left is 180 degrees ( pi radians ) and the line down is 270 degrees (3/2 pi radians)
You were correct to think of 9/4 pi radians as 2 pi radians plus 1/4 pi radians. Now, you have to find where 1/4 pi radians is, which is halfway between 0 radians and 1/2 pi radians ( 45 degrees )
What all the words mean is that every angle can be measured in a counter-clockwise direction (positive) or in a clockwise direction ( negative ). There fore + 45 degrees measured counter-clockwise from 0 degrees, is the same place as 45 - 360 = -315 degrees, measured clockwise form 0 degrees.
I hope this helps.

 

Harvey M