1)Well first off it is an identity. An identity is a proven fact or formula. The Pythagorean Theorem is an identity because it is a proven fact and forumla. Using x y and r we can see in letter b how the the Pythagorean theorem is written. Next we make the eaution eqaul to one by dividing by r^2 which leaves us with our final answer as seen in letter c. when we have it rewritten we see that x/r is a ratio for cosine on the unit circle and y/r is a ratio for sine on the unit circle. From this we can see how the unit circle plays into it.And from this information we conclude that cosine^2+sine^2=1. We add the sqaure because we can power these up.It is referred to as the pythagoreon identity because its just the theorem moved around a little. In letter h i chose 60 from the unit circle to prove that the identity is true.
2) In number two we have todervie the two remaining using what we came up with in letter f.In letter a i divided everything by cosine and what i was left with simplified to tan^2+1=sec^2 because what we had originally could be substituted using our identities. In b i did the same thing except this time i divided by sin^2.
Inquiry Activity Refelction
The connections that I see between Units N, O, P, and Q so far are that the unit circle comes into play alot of the time. From unit p we learned the basics of the traingles and how to find sides and angles and now we have taken it a step further with learning the law of sines and cosines. Also when we first learned how to graph angles in degrees and radians we use that for our word problems now.
If I had to describe trigonometry in THREE words, they would be difficult, puzzling, and usefull.
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