1) sin²x + cos²x = 1 is derived from the Pythagorean Theorem, which is, x² + y² = r².
When we divide r² from both sides, we get "1" on the right, and (x² / r²) + (y² / r²) = 1. We can make this into (x / r)² + (y / r)² = 1. We know that x/ r is sine, and y/r is cosine, so therefore we have sin²x + cos²x = 1.
2)
In the first picture, you divide cosine from each side, and end up with cos²x / cos²x + sin²x / cos²x = 1/ cos²x. this simplifies into 1 + tan²x = sec²x, and the second one is divided by sine, and you end up with 1 + cot²x = csc²x
Inquiry Activity Reflection
1) I connections that I see between Units N, O, P, and Q so far are that they all relate to one another. We start off by using the unit circle, then we basically derive the identities using the proofs in concept Q.
2) If I had to describe trigonometry in THREE words, they would be: Just Keep Practicing.
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