Do you like magic tricks? The following trick is appropriate for students who have studied the properties of trig functions.
Using a scientific calculator (in degree mode), compute sin -1 [sin([year born]-25)]. Assuming it is the year 2006, the result should be your age (or one year short if you have already celebrated your birthday).
Explain why this trick works (or doesn’t work).
Does the trick work on “all” scientific calculators?
Why must the calculator be in degree mode? Can you adapt the trick for radian mode?
How would you adjust the trick for use in a furture year (e.g. 2007)?
Hint: Try some other possible years of birth....be systematic, and look for patterns.
Solution Commentary: Some questions or hints to guide you further:
- What does the graph of y = sin -1 [sin([year born]-25)] look like?
- Using the hint provided, what is the earliest year that this trick will work? The last?
- What special properties of the f -1 (f(x)) are involved?
- Would the trick work if you used the expression sin[sin -1 ([year born]-25)]?
- Is the sin(a+b) expansion identity helpful?
- Think about the important roles of domains and ranges in this problem.