A Bit of An Update
After a period of inconsistent posts on this Substack Newsletter, I will now be posting and sharing maths puzzles on a regular basis. My tentative plan would be to publish a free newsletter on Wednesday, and a paid newsletter on Friday. The times for both will be 5:00 PM UK time.
The free newsletter contains more bite-sized maths puzzles at the high school and pre-university levels. These will be short to medium in length and should rekindle your love for mathematics.
The paid newsletter contains a wider range of topics at the undergraduate level. Subjects like analysis, linear algebra, multivariable calculus and differential equations will be explored through problem sheets and examples from my Warwick University lecture notes.
Anyway, let’s give this problem a try before jumping in for the solution!
Solution
We first consider the Pythagorean Identity.
We want to substitute the inverse cosine function for the angle theta.
We obtain the following.
Let’s look at our given curve.
How do we go from here? Pause and think.
Firstly, it should be evident that x can be written as the cosine of the inverse cosine of x.
Secondly, squaring our given expression results in what is shown above. Have you noticed what you can do yet?
Yes! In fact, it is the equation of the unit circle!
There is only an answer with a semi-circle because the inverse cosine function has range from 0 degrees to 180 degrees. This restricts the domain of the sine curve from only 0 to 1, and therefore, the answer is C.
Well done.
Leave any comments you have on alternate solutions!
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Happy reading,
Barry 🍩