an angle measuring (870n)° is in standard position. for which value of n will the terminal side fall on the…

Explanation:

Step1: Recall y - axis angle condition

Angles whose terminal side lies on the y - axis are of the form $90^{\circ}+ 180^{\circ}k$, where $k$ is an integer. We want to find $n$ such that $870n=90 + 180k$.

Step2: Simplify the equation

First, divide the equation $870n=90 + 180k$ by $30$. We get $29n = 3+6k$. Rearrange it to $29n-6k=3$. We can also think in terms of the remainder when $870n$ is divided by $360$. Angles on the y - axis have a remainder of $90^{\circ}$ or $270^{\circ}$ when divided by $360^{\circ}$. Calculate the remainder of $870n\bmod{360}$. $870\bmod{360}=150$, so we want $150n\bmod{360}$ to be either $90$ or $270$.

Step3: Test the values of n

For $n = 3$: $150\times3=450$, and $450\bmod{360}=90$.

Answer:

A. $n = 3$