I/D #3: Unit Q Concept 1: Pythagorean Identities

Inquiry Activity Summary


1.       The Pythagorean Identity comes from a derivation of the Pythagorean Theorem and we can basically call it an identity because it is a proven fact, which will be shown later in the work.

        From this picture we have the standard Pythagorean Theorem and we will be replacing it with trig functions. We use the values of sine and cosine in the side values and we use the hypotenuse of r which will always equal 1. We know this because we are solving with values from a unit circle. We then see that we can the whole thing by r which will basically leave it in the form known as one of the Pythagorean Identities. We then use 45° angle to prove this identity and thus fulfilling its definition, but how do we find the other two?


2.       The other two identities are found in just a few easy steps or rather one step and a few glances at the identities chart.

       As you can see we are really only dividing by sine or cosine and figuring out what each value produces in terms of different identities. So for example in the first part where we are trying to derive for the secant and tangent one, we find that tangent equals sin over cosine. 

Inquiry Activity Reflection

1. The connections that I see between Units N, O, P, and Q so far are that when we are deriving for these identities, we use values found on the unit circle from Unit N like the radius always equaling 1 which is very convenient for us. I also see a connection between P and Q because of the way we are deriving things from one to another reminds me of how we get the Law of Cosines and Law of Sines. It may seem like they are two entirely different things but they are actually connected together with a little math. 

2. If I had to describe trigonometry in three words, they would be connectable mathematical equations.