Sooo, this week in the SCC Vs. RA soccer game I went up for a header and some dudes teeth went in my head and split it open hahaha, so I missed the one thing I needed the most, the chapter 10 review. Oh well, I think I got this stuff for the most part. Right now I'm working on memorizing the hardest part in chapter 10 in my eyes.
10-3
Double-angle and half-angle formulas
sin 2(alpha) = 2sin(alpha)cos(alpha)
cos 2(alpha) = cos^2(alpha)-sin^2(alpha)=1-2sin^2(alpha)=2cos^2(alpha)-1
tan 2(alpha) = 2tan(alpha)/1-tan^2(alpha)
sin(alpha/2)= +- √(1-cos(alpha)/2) cos(alpha/2)= +- √(1+cos(alpha)/2)
tan(alpha/2)= +- √(1-cos(alpha)/1+cos(alpha))=sin(alpha)/1+cos(alpha)= 1-cos(alpha)/sin(alpha)
For a Decimal:use the half-angle formula to find alpha then multiply the decimal angle by 2.
One thing I don't really understand, and it seems like a lot of people don't understand this is knowing when to use the double and half angle formula.
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hey terrio, i hope you're feeling better.
ReplyDeletewe got specific notes on when to use the double and half angle formulas
ReplyDeletewhen you see a decimal you will use a double angle formula
but for deciding to use any formula is usually just a matter of looking at whats given because certian foumulas are called upon by specific equations or directions
you just have to look for the patterns
is you need more help on deciphering which formula to use feel free to ask me becasue i have found a few patterns myself
Here's an Example:
ReplyDeleteFind the exact value of sin22.5
alpha=2(22.5)
alpha=45
**if you are given an angle with a decimal you use the half-angle formula. To find alpha, you multiply by two.
the only time you use double angle formula is when things are being multiplied by 2.
ReplyDeletethe only time you use the half angle formula is when something is being divided by 2.