Period of Trigonometric Functions

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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(πœ‹x+3)
  11. 2cos(x/3+Ο€)
  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œ‹, πœ‹, 2πœ‹, 2πœ‹, πœ‹, πœ‹, πœ‹/2, 4πœ‹, 2, 6πœ‹, 2πœ‹, πœ‹, 4πœ‹, 2πœ‹, 2πœ‹]

Ideal Gases

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Question 11 in IB Physics November 2016 Paper 1 was a question on determining the gradient of the V-T graph for an ideal gas. Only 11% of candidates answered this question correctly and this statistic is the lowest in SL papers in the last 4 years. Why was this question so difficult? The correct alternative, C, has the same form as the most chosen alternative, B . Alternative B contains the gas constant R whereas alternative C contains the Boltzmann constant k, which is correct; 66% of candidates sitting for the paper confused the constants by selecting alternative B. This could have been avoided by using the formulae on page 6 of the Data Booklet. Make use of the Data Booklet in Physics examinations.