Monday, November 20, 2006
posted by michele h at 12:35 AM
On Friday, Ms. Armstrong has us do a little activity to help us understand how the trig functions relate to the y and x axis'. Whether it has a positive or negative value.

Here are some examples, that might help you understand:

SOH CAH TOA

(sinØ= opp/adj)

The sine function means that you need to divide the opposite by the adjacent. But instead of using the terms opposite and adjacent, what if there wasnt a degree for us to determine which side would be the opposite? We could use the Cartesian plane.

This is how you would write it:
sinØ =

the "r" in the denominator means radius
and the "y" means the distance in the y axis

In the example below, shows the two quadrants that contain positive sine values:

SINE RATIO



What factor contributes to the ratio being positive in those 2 quadrants? (What do those 2 quadrants have in common?)

the Y AXIS: as you can see in the diagram above, the two shaded quadrants are the two quadrants where the y value is positive.









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SOH CAH TOA

(cosØ= adj/hyp)

The cosine functions means you need to divide the adjacent by the hypotenuse. How would that be done on a Cartesian plane?

cosØ=

the "r" in the denominator means radius
and the "x" means the distance in the x axis

In the example below, shows the two quadrants that contain positive cosine values:

COSINE RATIO



What factor contributes to the ratio being positive in those 2 quadrants? (What do those 2 quadrants have in common?)

the X AXIS: as you can see in the diagram above, the two shaded quadrants are the two quadrants where the x value is positive.







_______________________________________

SOH CAH TOA





(tanØ= opp/adj)

The tangent function means you need to divide the opposite by the adjacent. How would that be done on a Cartesian plane?

tanØ=

which can also be shown like this:

tanØ=

the "x" in the denominator stands for the cosine which is related to the x axis

the "y" in the numerator stands for the sine which is related to the y axis

In the example below, shows the two quadrants that contain positive tangent values:

TANGENT RATIO




What factor contributes to the ratio being positive in those 2 quadrants? (What do those 2 quadrants have in common?)

This is a tricky one. Both values have the same sign. If you look at the diagram above you'll see that they're either in both positive, or both negative, so either the the answer will end up being a positive because a postive divided by a positive is positive. And a negative divided by a negative is negative.

HEY! this guy is so old and he's doing the same math as we are, it makes me feel like a genius! HAHA. Here click here to watch this video

Here's another video, it's pretty long and boring but it kind of helped me because it reviews the simple formula's of algebra enjoy ! (it even the pythagorean theorem, the way Ms. Armstrong showed it)

Well that's my short review on Cartesian Plane. Hmm.. who to pick next ?

I think I pick JEFF. Yeah, you are the winkest link. hehe :)



.. For some of the stuff above i used Ms. Armstrong's worksheet questions and materials. And yahoo was my source to find those videos
 



1 Comments:


At November 20, 2006 9:24 PM, Blogger Ms. Armstrong

Well...it looks like the old Michele is back. This is the kind of exceptional work that I'm used to getting from you. Nice to see you again.