Answer
a) A periodic function is a function that repeats itself on regular intervals.
b) Periods of sin(x), cos(x), sec(x), and csc(x): 2$\pi$. Periods of tan(x) and cot(x): $\pi$.
c) $\frac{1}{2}$
Work Step by Step
a) Definition of Periodic Function
b) When graphing these functions, we see a periodic pattern appear at regular intervals. For sin(x), cos(x), sec(x), and csc(x), it repeats for every interval of length 2$\pi$. For tan(x) and cot(x), it repeats for every interval of length $\pi$.
c) $sin(\frac{5\pi}{6})$ = $sin(\pi-\frac{5\pi}{6})$ = $sin(\frac{\pi}{6})$ = sin(30) = $\frac{1}{2}$.
