Periodicity — Practice Quiz

A Trigonometry cheat sheet for Periodicity — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Practice quiz

1. What is the value of $\sin(\frac{5\pi}{2})$?

   • $0$
   • $1$
   • $-1$
   • $\frac{\sqrt{2}}{2}$

   Answer: $1$

2. Simplify $\cos(7\pi)$.

   • $0$
   • $1$
   • $-1$
   • $\frac{1}{2}$

   Answer: $-1$

3. Which of the following expressions is equivalent to $\tan(x + 3\pi)$?

   • $\tan(x)$
   • $-\tan(x)$
   • $\cot(x)$
   • $-\cot(x)$

   Answer: $\tan(x)$

4. If $\sin(\theta) = 0.5$, what is $\sin(\theta + 4\pi)$?

   • $0.5$
   • $-0.5$
   • $0$
   • $1$

   Answer: $0.5$

5. Evaluate $\cot(-\frac{5\pi}{4})$.

   • $1$
   • $-1$
   • $0$
   • undefined

   Answer: $-1$

6. For which of the following functions is $f(x) = f(x + \pi)$ always true?

   • $\sin(x)$
   • $\cos(x)$
   • $\tan(x)$
   • $\sec(x)$

   Answer: $\tan(x)$

7. Given $\cos(\beta) = 0.8$, what is $\cos(\beta - 6\pi)$?

   • $0.8$
   • $-0.8$
   • $0$
   • $1$

   Answer: $0.8$

8. Which of the following angles has the same tangent value as $30^\circ$?

   • $210^\circ$
   • $150^\circ$
   • $330^\circ$
   • $-30^\circ$

   Answer: $210^\circ$

9. If $\alpha = \frac{\pi}{3}$, what is $\sin(\alpha + 10\pi)$?

   • $\frac{1}{2}$
   • $\frac{\sqrt{2}}{2}$
   • $\frac{\sqrt{3}}{2}$
   • $1$

   Answer: $\frac{\sqrt{3}}{2}$

10. Which of the following statements is FALSE?

    • $\sin(x + 6\pi) = \sin(x)$
    • $\cos(x - 8\pi) = \cos(x)$
    • $\tan(x + 5\pi) = \tan(x)$
    • $\sin(x + \pi) = \sin(x)$

    Answer: $\sin(x + \pi) = \sin(x)$