### Instruction: What is the period of $y = \csc x - \cos 3x$?### Response: To find the period of a trigonometric function, I need to look at the coefficients of x in the arguments of the trigonometric functions.
For the cosecant function, y = csc x, the coefficient of x is 1, so the period is 2π.
For the cosine function, y = cos 3x, the coefficient of x is 3, so the period is 2π/3.
Now, I need to find the least common multiple of 2π and 2π/3, because that is the smallest positive value of x that will make both functions repeat their cycles.
The least common multiple of 2π and 2π/3 is 2π, because 2π/3 is a factor of 2π.
Therefore, the period of y = csc x - cos 3x is 2π.