Period of Trigonometric Functions

A very common question in HSC Maths papers is to find the period of a given trig function. Some students regret putting the period of tan(x) as 2𝛑 in last year's HSC 2Unit paper! Here is a quick tutorial set on determining the period of trigonometric functions. Answers are given below.

1. sin(x)
2. 2cos(x)
3. tan(x)
4. csc(x)
5. sec(x)
6. cot(x)
7. 3sin(2x)
8. tan(2x)
9. cos(x/2)
10. sin(𝜋x+3)
11. 2cos(x/3+π)
12. cos(x)+sin(x)
13. cos(2x)+sin(2x)
14. cos(x/2)+sin(x/2)
15. sin(x)+sin(2x)
16. sin(x)+sin(2x)+sin(3x)

[2𝛑, 2𝜋, 𝜋, 2𝜋, 2𝜋, 𝜋, 𝜋, 𝜋/2, 4𝜋, 2, 6𝜋, 2𝜋, 𝜋, 4𝜋, 2𝜋, 2𝜋]