I found a book this morning containing a hexagonal figure of trigonometric ratios. It reminded me of the mnemonics I created when I was still in high school in order to remember the formulas during exams. Unlike in other countries, we were not allowed to have formula sheets during exams, so we have to memorize them all.
In the figure, any trigonometric ratio is a product of its immediate neighbors. Therefore, Continue reading
In this post, we discuss the proof behind one of the most commonly used identities in trigonometry. We examine the equations below and show why the relationships always hold.
To students who have taken trigonometry, I’m sure that you have met these equation before. The proof of these equations are as follows.
Consider triangle right angled at . From the definitions, we know that
Therefore, (1) and (2) .
Now, If we let , then , then substituting the values of and in (1) and (2), we have
and these are what we want to show.
As exercises, use the strategy above, or any strategy you want to prove the following identities.