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Monday, March 13, 2006

scribe # 23

Sup everyone Its Teddie again and today I'm doing my second scribe of the year. This week is going to be a good one with pi day and everything tomorrow. Well anyway lets get to the stuff we did today. Today was a 1 period so we start off in the afternoon. We go straight to the math dictionary: We continue to draw and put properties for the "other" trig functions. (Excluding sin and cos ). We finished writing down the stuff for tangent and cosecant.


THE SEACANT FUNCTION

secx = 1/cosx


Properties of the SEACANT function

Domain: { x x =/= pi/2 + k(pi); k E I, x E R}
Range: (-infinity, -1] U [1, infinity)
Amplitude: undefined
Period: 2pi
Roots: none
Y-intercept: y = 1
Symetry: even function
Asymptotes: pi/2 + k(pi); k E I


THE COTANGENT FUNCTION

cotx = 1/tanx or sinx/cosx


Properties of the COSEACANT Function

Domain: { x x +=/= k(pi); k E I, x E R}
Range: (-infinity, infinity)
Amplitude: undefined
Period: pi
Roots: pi/2 + k(pi); k E I
Y-intercept: none
Symetry: odd function
Asymptotes: k(pi); k E I

And thats all for our math dictionary today.
Now on to the stuff we learned:

In the diagram above is a right angle triangle with its hypotenuese congruent to the radius of the unit circle. Considering that we know what the value of the angle x, and that the hypotenuese is 1 (radius of unit circle). Finding the opposite side would be opposite/hypotenuese or sinx. Find the adjacent side would be adjacent/hypotenuese.

Considering the pythagrium theorum, (a^2 + b^2 = c^2)

this equation would be true

sin^2x + cos^2x = 1

Then we went over some questions

Solving Trig Identities (we first simplify and find a common graph)

(secx)(cotx)
=(1/cosx)(cosx/sinx)
=1/sinx
=cscx

To do this vice versa

cscx
=(1/sinx)(cosx/cosx) <-- multiply by 1 =(cosx/sinx)(1/cosx) =(cotx)(secx)

2 guidelines to consider:

1. rewrite the whole thing using sin and/or cos
2. work with complicated side 1st reduce and substitute as much as you can

Well thats all folks, and tomorrows lucky scribe is...............JANET!








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1 Comments:

At 3/14/2006 12:00 AM, Blogger Mr. Kuropatwa said...

Great scribe post Teddie!

Excellent use of colour and and your explanations are really clear. I seem to remember stumbling in class a little bit today ... thanks for correcting (covering up) my mistakes. ;-)

 

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