### 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!

## 1 Comments:

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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