Responses Essay Sample

While it is a good practice to display the trigonometric identities in order to become more familiar with them, it would be better practice to work on some basic identities in order to come up with the other identities. For instance, the Pythagorean identity can be transformed into the other identities. This identity can be divided by the square of sin θ in order to obtain cot²θ + 1 = csc²θ. If tan x = sin x/cos x, then as cot x = 1/tan x, then cot x = cos x/sin x. Furthermore, being able to solve trigonometric problems such as trigonometric equations sometimes requires the application of identities, and so, as in all mathematics, practice makes perfect. The identities posted near one’s study area will be there to guide the student until he is able to navigate through his own solutions.
The cheat sheet that was given in the post is indeed very comprehensive and helpful. It is really a one-stop shop for problem solving in trigonometry. But just like the recommendation above, it would be very helpful to see and understand the relations between and among the different sets of identities, and how one set could lead to another. How sin (A+B) can be used to derive sin 2A or sin 2B would make for an interesting exercise as well. Also, why an identity is so must be understood. If -sin x = sin(-x), and the function is an odd one, what makes it odd aside from this requirement? The student must always be able to understand this very well, so that he can apply the identity properly and clearly. Beyond memorizing the identity, one must be able to understand why he is making use of the identity in the first place.