an angle measuring (525n)° is in standard position. for which value of n will the terminal side fall on the…

Explanation:

Step1: Recall angle - position condition

Angles whose terminal side lies on the (y) - axis are of the form ((90 + 180k)^{\circ}), where (k) is an integer. We need to find (n) such that (525n=90 + 180k).

Step2: Simplify the equation

First, rewrite the equation (525n=90 + 180k) as (105n = 18+36k) (dividing by 5). Then (35n=6 + 12k). We can check each value of (n) by substituting.

For (n = 2):

(525\times2=1050^{\circ}), (1050\div360 = 2) full - rotations ((2\times360 = 720^{\circ})) plus (1050 - 720=330^{\circ}), not on the (y) - axis.

For (n = 3):

(525\times3 = 1575^{\circ}), (1575\div360=4) full - rotations ((4\times360 = 1440^{\circ})) plus (1575 - 1440 = 135^{\circ}), not on the (y) - axis.

For (n = 5):

(525\times5=2625^{\circ}), (2625\div360 = 7) full - rotations ((7\times360=2520^{\circ})) plus (2625 - 2520 = 105^{\circ}), not on the (y) - axis.

For (n = 6):

(525\times6 = 3150^{\circ}), (3150\div360=8) full - rotations ((8\times360 = 2880^{\circ})) plus (3150 - 2880=270^{\circ}), and (270^{\circ}) has its terminal side on the (y) - axis.

Answer:

(n = 6)