Question

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

Answer 1

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 $(90^0)a$

Where a = positive odd integer,

We hyave given the given angle is,

$(870n)^0,$

What is terminal side?

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

$(870(3))^0=2610^0$

The  angle will be 2610°

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

$2610^0 = (90^0)a \implies a = 29$......( 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,

$3480^0 = (90^0)a \implies a = 38.6667 ( Not possible )$

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,

$4350^0 = (90^0)a \implies a = 48.333.. ( Not possible )$

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,

$5220^0 = (90^0)a \implies a = 58..... ( Not possible )$

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