Step 1 :The sine, cosine, cosecant, and secant functions are periodic functions with a period of $2\pi$. This means that the function repeats its values every $2\pi$ radians.
Step 2 :On the other hand, the tangent and cotangent functions have a period of $\pi$. This means that these functions repeat their values every $\pi$ radians.
Step 3 :Final Answer: The sine, cosine, cosecant and secant functions have period \(\boxed{2\pi}\) : the tangent and cotangent functions have period \(\boxed{\pi}\).