Saturday, March 22, 2008

Proving Identities with cos and sin

Hey everybody, this is Paul, posting the scribe post for our Thursday class which was on the 20th. Sorry this is so late, its been a hectic week.

Note: This is the symbol for theta in my blog post: Θ.

Okay, so Thursday we continued the topic of using identities with sin and cos and expanded it so we could prove stuff like sin(pi/6+Θ) + sin(pi/6-Θ) = cosΘ. This is demonstrated in our 2nd slide.

At first the solution confused me, but I realized the solution works by using the formula we used previously to convert a formula that looks like:
sin(α+β) + sin(α-β) = cosβ

And use formulas we already know to convert it to:

(sinαcosβ + cosαsinβ) + (sinαcosβ - cosαsinβ)

And then reduce to get cosΘ.

In slide 3, we were given a question that asked us to find the cosine of alpha (cosα) and the sin of beta (sinβ). Initially, we got the wrong final answer because we made the mistake of saying that α = -3/5, which is WRONG.

The truth is we never get the value of alpha, we only get the value of the cosine of alpha.

Once we realized our error, we solved the problem properly by using the formula cos(α+β) = cosαcosβ - sinα+sinβ, giving us the correct answer of -33/45. The proper solution is on slide 4.

After that, we were given the same question except we were told to solve for sin(α+β). This takes place on slide 5. The solution is pretty straightforward since you just change the formula but keep all the values you already found in the previous question.

Mr.K then started talking about his "clever idea." He explained to us that the R, Q, and P can be defined in terms of sin and cos on slide 6. He then started to talk about the values of cos and sin in the rotated triangle, but didn't finish because the class ended. I guess we'll find out how clever his idea is on Monday.

Slide 7 shows us how to rotate a point 90 degrees in terms of coordinates. If your coordinates are (x,y) unrotated, then when you rotate it 90 degrees your coordinates will be (-y,x) (such that x = -y and y=x). For 180 degrees, your outcome would be (-x,-y).

And the sums up my scribe post. Sorry it took so long to be posted, especially since its rather short. I didn't manage to get around to doing it until now.

And since nobody's told me they want to be scribe, I will randomly choose a name from a hat (in my mind).

The lucky winner is... ZEPH.

And colour me surprised, the name's not in pink. (gasp)
Somehow it still stands out from the rest of the post.

Good night and farewell.

P.S. And Mr.K, I think the scribe list needs some updating?

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