Question

What is the reference angle of 9pi/4 and 3pi/7
What is the reference angle of 9pi/4 and 3pi/7
@Mathematics

Answer 1

pi/4

Answer 2

Suppose you have an angle theta and want to find the reference angle. The first thing you should do is find an equivalent angle in the range 0 <= new theta < 2pi. This is easy to do...

If theta >= 2pi, then keep subtracting 2pi from theta until it is within range (remember, 2pi is one full revolution on the circle).

Likewise, if theta < 0, keep adding 2pi to it until it falls within range.

Once you have your new value of theta, compute the reference angle as follows:

If the new theta is in the 1st Quadrant, then ref angle = theta.
If the new theta is in the 2nd Quadrant, then ref angle = pi - theta.
If the new theta is in the 3rd Quadrant, then ref angle = theta - pi.
If the new theta is in the 4th Quadrant, then ref angle = 2pi - theta.

So let's do your problems...

9pi/4 = (9/4)pi = (2.25)pi > 2pi

So subtract 2pi from it to obtain a coterminal angle.

(9/4)pi - (8/4)pi = (1/4)pi = pi/4

That falls within range, so your new theta is pi/4. Pi/4 is in the 1st Quadrant, so the reference angle is pi/4.


3pi/7 is already within range. This angle is also in the 1st Quadrant (3/7 < 1/2, so 3pi/7 < pi/2), so the reference angle is 3pi/7

Answer 3

thanks...