how to get the next two positive angles for each:
1.) \frac{7\pi}{6}
2.) \frac{4\pi}{5}
To find the next two positive angles for each given angle, you can use the following formula:
Next angle = Given angle + 2π
For the first angle, π is equal to 180 degrees, so we can rewrite the formula as:
Next angle = Given angle + 2(180 degrees)
Now, let's find the next two positive angles for each given angle:
1) Given angle = 7π/6
Next angle = 7π/6 + 2(180 degrees)
= 7π/6 + 2(π)
= 7π/6 + 2π
= 7π/6 + 12π/6
= 19π/6
The first next positive angle is 19π/6. To find the second next angle, we apply the formula again:
Next angle = 19π/6 + 2π
= 19π/6 + 12π/6
= 31π/6
So, for the angle 7π/6, the next two positive angles are 19π/6 and 31π/6.
2) Given angle = 4π/5
Next angle = 4π/5 + 2(180 degrees)
= 4π/5 + 2(π)
= 4π/5 + 2π
= 4π/5 + 10π/5
= 14π/5
The first next positive angle is 14π/5. To find the second next angle, we apply the formula again:
Next angle = 14π/5 + 2π
= 14π/5 + 10π/5
= 24π/5
So, for the angle 4π/5, the next two positive angles are 14π/5 and 24π/5.