Period of Trig Function 2

What is the relationship between the coefficient before x (usually called b) and the period? How do you calculate the period if you know the value of b?
How can equivalent fractions help you find more possible answers?
Could you also consider improper fractions?

The coefficient before x is the frequency of the periodic function. To find the period you do 360/b. If b=1/2 you do 360 / (1/2) which equals 720. Unfortunately, this is not a possible answer, since it uses the number 2 twice. However, we can use equivalent fractions to 1/2 to find solutions that do work, for example:

y = sin 3/6x and period: 720°
y = sin 4/8x and period: 720°

b=1/3 results in a 4-digit period, however we can use b=2/3 and its equivalent fractions:
y = sin 2/3x and period: 540°
y = sin 6/9x and period: 540°
y = sin 4/3x and period: 270°
y = sin 5/3x and period: 216°
y = sin 6/3x and period: 180°
y = sin 9/3x and period: 120°

Along with many more possible answers.