Determine two coterminal angles (one positive and one negative) for the given angle. Give your answer in radians.

A) 8pi/9 B) 8pi/45

For 8pi/9 I added 18pi/9 which equals 26pi/9 - 18pi/9 = -10pi/9.

I do not know how to find the positive one for 8pi/9 and I do not know what to do for b.

To find the positive coterminal angle for 8pi/9, you can add a full revolution of 2pi radians to the angle:

8pi/9 + 2pi = 16pi/9

So, one positive coterminal angle for 8pi/9 is 16pi/9.

For 8pi/45, you can also add multiples of 2pi to find coterminal angles. However, it is more helpful to find an equivalent angle within the interval [0, 2pi). You can do this by dividing the angle by its common factor, which is pi/45.

(8pi/45) / (pi/45) = 8

So, an equivalent angle within the interval [0, 2pi) for 8pi/45 is:

8 * pi/45 = 8pi/45

Therefore, one positive coterminal angle for 8pi/45 is 8pi/45.

To find the positive coterminal angle for 8π/9, you need to keep adding or subtracting 2π (or any multiple of 2π) until you reach a positive angle that is coterminal with 8π/9.

Starting with 8π/9:
1st coterminal angle: 8π/9 + 2π = 10π/9 (positive angle)
2nd coterminal angle: 10π/9 + 2π = 22π/9 (positive angle)

Therefore, the positive coterminal angles for 8π/9 are 10π/9 and 22π/9.

Now let's move on to B) 8π/45:

To find the positive coterminal angle for 8π/45, you follow the same process of adding or subtracting 2π until you reach a positive angle that is coterminal with 8π/45.

Starting with 8π/45:
1st coterminal angle: 8π/45 + 2π = 358π/45 (positive angle)
2nd coterminal angle: 358π/45 + 2π = 716π/45 (positive angle)

Therefore, the positive coterminal angles for 8π/45 are 358π/45 and 716π/45.

Keep in mind that when you're adding or subtracting the multiples of 2π, you need to simplify the result if possible. In some cases, you might end up with fractions or mixed numbers.