Question

An angle measuring (870n)° is in standard position. For which value of n will the terminal side fall along the positive portion of the y-axis?
n = 3
n = 4
n = 5
n = 6

Answer 1

The answer would be n=3

Answer 2

Answer:  

n = 3

Step-by-step explanation:

The terminal side of an angle fall along the positive portion of the y-axis,

If it can written in the form of (90°)a

Where a is any positive odd integer,

Here, the given angle is,

(870n)°,

For n = 3,

Our angle will be 2610°

Its terminal side fall along the positive portion of the y-axis,

If 2610° = (90°)a ⇒ a = 29 ( Positive odd integer )

Thus, 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,

If 3480° = (90°)a ⇒ a = 38.6667 ( Not possible )

Thus, for n = 4, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis

For n = 5,

Our angle will be 4350°

Its terminal side fall along the positive portion of the y-axis,

If 4350° = (90°)a ⇒ a = 48.333.. ( Not possible )

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,

If 5220° = (90°)a ⇒ a = 58 ( Not possible )

Thus, for n = 6,  the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis.