Junior Certificate Examination 2011 Sample Paper Mathematics Page 19
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24Question 15
(Suggested maximum time: 10 minutes)
During a trigonometry lesson a group of students write down some statements about what they
expected to happen when they look at the values of trigonometric functions of some angles. They
then find the Sin, Cos and Tan of some angles, correct to three decimal places, to test their ideas.
Here are some of the things they wrote down.
The value from any of these trigonometric functions will always be less than 1.
(i)
(ii)
If the size of the angle is doubled then value from the trigonometric functions will not double.
(iii) The value from all of the trigonometric functions will increase if the size of the angle is
increased.
(iv) I do not need to use a calculator to find Sin
60 . I can do it by drawing an equilateral triangle.
°
The answer will be in surd form.
(a)
Do you think that (i) is correct? Give an example to justify your answer.
Answer:
Example:
(b)
Do you think that (ii) is correct? Give an example to justify your answer.
Answer:
Example:
(c)
Do you think that (iii) is correct? Give an example to justify your answer.
Answer:
Example:
(d)
Show how an equilateral triangle of side 2 cm can be used to find Sin
60 in surd form.
°
Sin
60 =
°
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Junior Certificate 2011 – sample paper
Page 19 of 23
Project Maths, phase 1
Paper 2 – Higher Level
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