The value of n will the terminal side fall on the y-axis at n=3
The terminal side of an angle fall along the positive portion of the y-axis,
If it can written in the form of
Where a = positive odd integer,
We hyave given the given angle is,
![(870n)^0,](https://tex.z-dn.net/?f=%28870n%29%5E0%2C)
<h3>What is terminal side?</h3>
The terminal side of an angle theta drawn in angle standard position is the side which isn't the initial side
Now for n=3
![(870(3))^0=2610^0](https://tex.z-dn.net/?f=%28870%283%29%29%5E0%3D2610%5E0)
The angle will be 2610°
Its terminal side fall along the positive portion of the y-axis,
......( Positive odd integer )
Therefore for n = 3, the terminal side of the angle (870n)° falls along the positive portion of the y-axis,
For n = 4,
Our angle will be 3480°
Its terminal side fall along the positive portion of the y-axis,
![3480^0 = (90^0)a \implies a = 38.6667 ( Not possible )](https://tex.z-dn.net/?f=3480%5E0%20%3D%20%2890%5E0%29a%20%5Cimplies%20a%20%3D%2038.6667%20%28%20Not%20possible%20%29)
Therefore for n = 4, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis
Next is for n = 5,
Our angle will be 4350°
Its terminal side fall along the positive portion of the y-axis,
![4350^0 = (90^0)a \implies a = 48.333.. ( Not possible )](https://tex.z-dn.net/?f=4350%5E0%20%3D%20%2890%5E0%29a%20%5Cimplies%20a%20%3D%2048.333..%20%28%20Not%20possible%20%29)
Thus, for n = 5, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis,
For n = 6,
Our angle will be 5220°
Its terminal side fall along the positive portion of the y-axis,
![5220^0 = (90^0)a \implies a = 58..... ( Not possible )](https://tex.z-dn.net/?f=5220%5E0%20%3D%20%2890%5E0%29a%20%5Cimplies%20a%20%3D%2058.....%20%28%20Not%20possible%20%29)
Thus, for n = 6, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis.
Therefore,the value of n will the terminal side fall on the y-axis at n=3.
To learn more about the terminal side visit:
brainly.com/question/24680641