Scribe post, 4/27/10

We started with a warm up where we had to
1. Solve on [0,2π)
sin2x-cosx=0
2. Find the exact value of cos105˚
3. Use the figure to find tan2u
















We went over how to figure out if our answer is right when we finally get an answer.
For number 1
sin2x-cosx=0
2sinxcosx-cosx
cosx(2sinx-1)=0
so cosx = 0 and sinx = 1/2


for number 2
cos(105˚)

we then went over the Law of Sines which is and
we started deriving the law of sines

then we proved that they are all equal for all triangles

We also talked about the added bonus which is

we tried this on a random triangle from GeoGebra where (using AAS therom)
A=59.85˚
C=26.05˚
c=4.78 units

so B =180˚-A-C
B=94.1

so a = 9.41

b=10.86
for the last 10 minutes of class we did our homework

Scribe post

I'm sorry this is late but I've been having troubles with this posting thing.
To start the class we did a warm up where we had to evaluate

cos^-1(√3/3)
a) you would be looking for an angle and since you are looking for an angle where the inverse cos is a -√(3)/2 then it would be 150˚it is also possible to get an answer of 5π/6 algebraically you could do x=cos
cosx=-√3/2
sin(cos^-1 √5/5)
b) in this one the answer will be a ratio ø=cos^-1 sqrt(5)/5
cosø=sqrt(5)/5 sinø=(√20)/5

we also had to evaluate the graphs of
y=arscin(x-1)
a)y=arcsin(x-1) this is just a sin graph only with the restricted domain to make it a function and the negative 1 makes it move 1 unit to the right and the minimum and maximum is π/2
y=tan(3x-6/π)
b) you can set this up as an inequality because the period of tan is π so -π/2<3x-π/6<π/2>2π/9 y="sec^-1" secy="x" cosy="1/x" y="arccos^-1(1/x"

Unit 3 logarithms, Scribe post, Collin Downs

Today we started class with the super correction follow up test for the first 25 minutes of class. We then jumped to (1+1/x)^x which is also called e and what happens to it when it gets very large and how neither the base or the power wins and makes the function go towards 1 or a large number. We used this to show the transformation from A=P(1+r/n)^nt to A=Pe^rt because you can substitute n/r for x and 1/x= r/n so you can substitute e for 1+r/n and get A=Pe^rt. We then went on to homework where we talked about #21 with reference to the purple math visual of turning a log into an exponential. The last thing we learned today was the big three log properties with reference to the mystery function worksheet.
1. log(a*b)=log(a) * log(b)
2. log a^n= n*log a
3. log a/b= log a - log b
These will be used in our homework tonight which is p. 243/11-45 odd, 61-67 odd.