INQUIRY ACTIVITY SUMMARY
1. Where does where sin2x+cos2x=1 come from to begin with (think Unit Circle!). You should be referring to Unit Circle ratios and the Pythagorean Theorem in your explanation.
A: Well first we should ask ourselves what is an identity? And why the Pythagorean Theorem is also an "identity"? An identity are proven facts and formulas that are always true. Then, we should ask ourselves what is the Pythagorean Theorem using x, y, and r? Well it's x^2+y^2=r^2 divided by r^2, which then makes the operation equal to 1. Remember what the ratios are for cosines and sines are in the unit circle. Cosine is (x/r) and Sine is (y/r) and you're able to see that cos^2ø+sin^2ø=1. It's referred to an identity because it's a formula that's always true. For example, (√3/2,1/2) cos30º = (√3/2)^2 = 3/4 and sin30º= (1/2)^2 = 1/4. Cos^2ø+Sin^2ø=1.
2. Show and explain how to derive the two remaining Pythagorean Identities from sin2x+cos2x=1. Be sure to show step by step.
A: So first off with we know that sin^2x +cos^2x=1, then you have to divide cos^2x to both sides and that gets you tan^2x+1=sec^2x. And then for the other one we know that sin^2x +cos^2x=1 and now all we have to do is divide sin^2x and we get csc^2x.
INQUIRY ACTIVITY REFLECTION
“The connections that I see between Units N, O, P, and Q so far are…” is that the problems that we work with happen to be similar. For example, the Pythagorean theorem somehow always manages to come out.
“If I had to describe trigonometry in THREE words, they would be…” awe-struck, mind-blowing, and fun.
No comments:
Post a Comment