Conics- major / minor axis ( from formulas) - Transverse / conjugate axis

For ellipses, you have two axis, a major and a minor . the major axis is always the longer of the two ( see video, starts on ellipses).





For Hyperbolas, you also have two axis, a transverse axis and a conjugate axis. ( see video, after ellipses)





Transverse axis


-connects verticies


-not always longer than conjugate axis


- length is alwas 2a units (a+a)


- there for length of conjugate is always 2b units (b+b)

natural logarithms(-notations-equations-and applications)

REMEMBER! loge = ln





OK, for this first slide he used 3 logarithmic identities to form the single logarithm
1. ln(x-1) + 3ln(x+3) becoming the numerator(x-1)(x+3)^3 from
the identity log e (MN)= log e M + log e N

2.from (ln(x-1)+3ln(x+3))-1/2ln(x^2+2) he got the denominator Square Root of (x^2+2) which is the same as(x^2+2)^1/2 from the identity log e (M/N) = log e M - log e N

3. and the third identity is log e (M^N) = N log e M which you can see done with both the numerator and denominator




the only thing i think i need to explain with this one is that if both sides of an equation have loge
in front we know we can take it away, correct? so i guess the opposite can be done as well where we add in loge, which is seen done in the second line (the red ink).


(remember! loge = ln)!



*lne=1


this slide uses the third identity mentioned in the first slide, and takes away ln from both sides(as mentioned in slide two), other than that i think it is self explanatory.




in this slide he adds ln to both slides making lne on the left side which previously stated equals one(see lime green * in above slides explination).

and again he used the third identity mentioned in slide 1.

Hope this helped you in anyway, shape, or for possible


Mr. Maksymchuk gave use another one of his shirt ideas this one was based on the Pink Floyd album cover the dark side of the moon with the rainbow and prisms, but his shirt would say Pink Freud. I didn't get the reference but maybe you did.


I later googled it and it was referanced to Sigmund Freud who was a phsycoanalysis who was best know for his theories of the unconcious mind and the defence mechanism of repression.


after all that i still didn't completely get it, oh well, my loss I guess

Trig Identities (more notes, examples,etc..)

Mr. Max says that trig identities is basically the same as solving puzzles in class
there is never the solution only a solution

Techniques to assist proving identities

1.reduce (simplify complicated side to try to "match" the simpler side)

2.work each side independently to some intermediate expression

3. DO the addition / subtraction of the rational expressions.

4.DO the multiplication / division of the same rational expressions.

5. Simplify GCF's ALWAYS (ie. factor if you can)

6. Factor, Factor, Factor

7.try multiplying both numerator / denominator by same expression to get to know identities.

8. IF possible? rewrite all trig. functions as sin(x) or cos (x);look for patterns

Todays assignment is exercise 15 questions 1-14

Solving Trig equations over Real Numbers

In today's class, in addition to solving trig equations over a set domain, we also learned the process of solving trig equations over real numbers.

In any case the answer over all reals will be what ever radian you get, plus 2 pie multiplied by K, where K is any integer

For home work we were assigned Exercise 5 questions 1 through 12.

Our test is on Thursday Oct 1st, one week from today.

At first this stuff had me completely lost but the more Mr.max explained it the easier it got.

I call January 2007 # 20 in the multiple choice

A is the answer!

so 1 over x is what we want

Thus we get

But It would seem as if they don't want the rationalized answer.

The answer would be A because the x value is negative