Find a negative and a positive coterminal angle for Ө = 2pi/3.
-4pi/3 and 8pi/3
Ah, 2pi/3, the angle that's about as popular as pineapple on pizza! Now, if you're looking for some coterminal angles, well, grab your sense of humor because I've got a negative and positive coterminal angle just for you!
For a negative coterminal angle, we can go a full revolution in the clockwise direction. So, hang on tight, because we're heading down to -4pi/3! It's like taking a detour when you're already lost, but hey, we're getting there, right?
Now, if we want to keep things positive, let's go ahead and do a full revolution in the counterclockwise direction. We're going beyond the norm here! Brace yourself for 8pi/3, the angle that's so positive it starts throwing confetti and celebrating itself!
So, there you have it - a negative coterminal angle of -4pi/3 and a positive coterminal angle of 8pi/3. Just remember, when life throws you angles, make sure to keep your sense of humor handy!
To find a negative coterminal angle for θ = 2π/3, you can subtract 2π from the angle repeatedly until you get a negative angle.
So, subtracting 2π from 2π/3, we get:
2π/3 - 2π = -4π/3
Therefore, the negative coterminal angle for θ = 2π/3 is -4π/3.
To find a positive coterminal angle for θ = 2π/3, you can add 2π to the angle repeatedly until you get a positive angle.
So, adding 2π to 2π/3, we get:
2π/3 + 2π = 8π/3
Therefore, the positive coterminal angle for θ = 2π/3 is 8π/3.
To find a negative coterminal angle, subtract 2π from the given angle:
2π/3 - 2π = 4π/3
Therefore, -4π/3 is a negative coterminal angle for Ө = 2π/3.
To find a positive coterminal angle, add 2π to the given angle:
2π/3 + 2π = 8π/3
Therefore, 8π/3 is a positive coterminal angle for Ө = 2π/3.
So the negative coterminal angle is -4π/3 and the positive coterminal angle is 8π/3.
A = 2pi/3 = 360/3 = 120o.
120-360 = -240o.