Well todays class, in my opinion went very quick yet it was compact because we were introduced a new topic in math today called Proofs of the Sum and Difference Identities.
First we started off the class with the usual identities problems. Nothing new there because it was all straight forward unless if you havent been doing your homework.
OK now onto math!
I know its a crappy picture but you can see it in todays slides none the less you should be able to recognize it.
1. Given sinA= 4/5 cosB=-5/13. With cosA<0>0. Find cos(A + B)
-The best start off for this question is to draw a diagram which we have done, just so it makes it easier to determine the equation that we will be using later on.
-Now, since we are trying to find cos(A + B) we will write the rest of the equation that goes along with it.
Recall:
Its the sine dance! The equation that goes along with cos(A +B) is written as: cos(A + B)= cosAcosB - sinAsinB
-Then we plug in the specified #'s from the diagrams we drew. So cosA is (-3/5) because in the alpha diagram the cosA is adjacent over hypotenuse. just keep plugging in the numbers for the rest of the equation.
-Once your done writing out the rest of the equation work them out by getting the common denominator. You should end up with the answer -33/65. Which results with the answer being in Quad. III.
Now its nearing the end of class and he quickly introduced Proofs of the Sum and Difference Identities.
If we rotate diagram 1 so that R equals 90 degress and P is on the axis it will look like diagram 2. pretty much everything shifts clockwise.
Q'P' = QP
Now what we have to do is find the distance from Q'P' by using the distance formula:
= √((cos A- B) - 1)² + ((sin A - B) - 0)²
= √(cosA - cosB)² + (sinA - sinB)²
Around here Mr.K was totally rushing everything haha. Trying to finish the question before the bell rang. I didn't really understand a word he said after this plus I could no longer see the smart board cuz he was so busy writing.
Besides the end of the class it was pretty ok math that we learned today. Very understandable. Hope you got something out of my blog.
Drum roll please. "Attention! The next scribe is..........Derek!" ( I picked it randomly!)
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