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

The answer is n=3

Step-by-step explanation:

Given that an angle measuring (870n) ° is in standard position.

we have to find the value of n for which the terminal side fall on the y-axis.

If it can written in the form of (90°) a, where a is any positive odd integer.

The terminal side fall on y-axis when a is 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.