So we're now done our third unit, the unit of identities. I think this unit began quite quickly, and lots of information was just thrown at us (especially for me since I wasn't there for the first class of Identities). But as the unit progressed, I think we kind of moderated our learning pace and things began to become more clear and visible in my mind. Mr. K was right, and throughout my bob I'll probably stress it repeatedly, practice is the only way to get good at identities. Homework in this unit is especially beneficial to understanding how to manipulate identities and mathematically "massage" them accordingly. If you payed attention and continued with your homework regularly, I don't think this unit would be particularly difficult. Don't forget, practice is the only way!!! So, overall, this unit went by extremely quickly, but for the amount of material we learned I think we went at well-regulated pace. In essence this unit wasn't too difficult, particularly if you kept up with your homework. There isn't much more to say, so I'll end this bob with a list of the common identities you should know for the test. They are as follows:
- sin2θ + cos2θ = 1
(note: you can derive other equations by dividing every term by either sin2θ or by cos2θ, which will give:
tan2θ + 1 = sec2θ and 1 + cot2θ = csc2θ)
- tanθ = sinθ / cosθ
- cscθ = 1/sinθ
secθ = 1/cosθ
cotθ = 1/tanθ or cosθ/sinθ
- remember the sine dance :
sin(α+β) = sinαcosβ + cosαsinβ (change sign for α-β)
cos(α+β) = cosαcosβ - sinαsinβ (change sign for α-β)
- don't forget to watch for a difference of squares!
GOOD LUCK ON THE TEST AND PRETEST EVERYONE!! DON'T FORGET TO PRACTICE THOSE IDENTITIES!