Given: Measure of angle = (468 n)°
To Find: The value of n for which the terminal side fall on the x-axis
Solution:
Angle =(468 n)°
for , n=1
Angle = 468°= 360°+108°→108°> 90°(Second quadrant)
for, n=2
Angle = 468°×2=936°=720°+216°→216°> 180°(Third quadrant)
For, n=3
Angle = 468°× 3 = 1404°=1080°+324°→324°>270°(Fourth quadrant)
For, n=4
Angle = 468°× 4 = 1872°=1800°+72°→72°(First quadrant)
For, n=5
Angle = 468°× 5 = 2340°=180°×13→Falls on X axis.
Alternative Method:
(468 n)°=90° k
n=
, so if k is a multiple of 26 , we get different values of n.
Smallest value of n for which terminal side fall on the x-axis is when (k=26, n=5), (k= 52, n=10),......