Precalculus Help...I know, I'm a noob :(

swetooth9

swetooth9

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anyway, i'm probably sure i'm just not thinking of the right "combination" for lack of a better word...

here's a problem i'm stuck on:

simplify this...

1 - [ (cot^2 X + cot X) / (cot^2 X - 1) ] + 3

the answer should be either 3cotX - 4 or (3cosX - 4sinX) / (cosX - sinX)

the thing is, i have to show work, so i need help

if anyone is willing, thanks!
 
[quote name='swetooth9']anyway, i'm probably sure i'm just not thinking of the right "combination" for lack of a better word...

here's a problem i'm stuck on:

simplify this...

1 - [ (cot^2 X + cot X) / (cot^2 X - 1) ] + 3

the answer should be either 3cotX - 4 or (3cosX - 4sinX) / (cosX - sinX)

the thing is, i have to show work, so i need help

if anyone is willing, thanks![/QUOTE]
Ok...

1=> 1 - [ (cot^2 X + cot X) / (cot^2 X - 1) ] + 3

2=> 4 - [ (cot^2 X + cot X) / (cot^2 X - 1) ]

3=> 4 - [ {cotx(cotx + 1)} / (cotx + 1)*(cotx - 1) ]

4=> 4 - [ cotx / (cotx -1) ]

5=> [4cotx - 4 - cotx] / [cotx - 1]

6=> [3cotx - 4] / [cotx - 1]

7=> [(3cosx - 4sinx) / sinx) / (cosx - sinx) / sinx

8=> (3cosx - 4sinx) / (cosx - sinx)

edit: if you can't see what I did on a step, let me know.
 
I would have been able to answer a couple months ago, but that was last semester. My brain can only handle so much math, and right now it's on matrices.

Good luck.
 
[quote name='swetooth9']wait what did you do b/t steps 4 and 5?[/QUOTE]
Multiplied that 4 out front up and down by (cotx - 1) so the whole thing would be over the same denominator.
 
ohhhhhhhh, ok thanks, jmcc! :D

i didnt see that the bottom could be factored out until you showed me...i knew there was something i missed

thanks!
 
[quote name='swetooth9']ohhhhhhhh, ok thanks, jmcc! :D

i didnt see that the bottom could be factored out until you showed me...i knew there was something i missed

thanks![/QUOTE]
Sure, no problem.

edit:
[quote name='swetooth9']willing to tackle another one? haha[/QUOTE]
As my teacher says "I'm not sure, maybe I can do these." He's a pretty big smartass for such an old guy. But sure, what's the problem.
 
the problem is:

(sin^3 X - cos ^ 3 X) / (1 - sin^2 X cos^2 X)

i simplified it all the way down to:

(sinX - cosX) / (1- sinX cosX) (1 + sinX cos X)

but i dont know what to do next
 
[quote name='swetooth9']the problem is:

(sin^3 X - cos ^ 3 X) / (1 - sin^2 X cos^2 X)

i simplified it all the way down to:

(sinX - cosX) / (1- sinX cosX) (1 + sinX cos X)

but i dont know what to do next[/QUOTE]
What's it supposed to look like at the end?
 
[quote name='swetooth9'](sinX - cosX) / 1 - sinXcosX

or

1 + sinXcosX[/QUOTE]
Sorry this took so long, I was being a dope about it. Did you see how you do it yet? Split the top up as a difference of cubes. Then take the 3 term poly and change (sinx)^2 into 1-(cosx)^2 (or do the sin squared like that, too) which gets that 3 term down to 1 + sinxcosx. Then you can eliminate and you're left with (sinx - cosx) / (1 - sinxcosx).
 
umm, yea, would you mind doing the steps thing since it's hard to understand it in a paragraph...i'm not sure if i did the difference of cubes correctly
 
I'll work the parts seperately.

sinx^3 - cosx^3 / 1 - sinx^2cosx^2

Top: sinx^3 - cosx^3

= (sinx - cosx)(sinx^2 + sinxcosx + cosx^2)

= (sinx - cosx)(sinx^2 + sinxcosx + [1 - sinx^2])

= (sinx - cosx)(1 + sinxcosx)

Bottom: (1 - sinx^2cosx^2)

= (1 - sinxcosx)(1 + sinxcosx)

So the (1 + sinxcosx)'s on top and bottom cancel and you're left with (sinx - cosx) / (1 - sinxcosx).
 
Converting (cos x)^2 into 1 - (sin x)^2 is a waste of time, it would of be easier to reconized that (cos x)^2 + (sin x)^2 = 1.
 
[quote name='Dkellar']Converting (cos x)^2 into 1 - (sin x)^2 is a waste of time, it would of be easier to reconized that (cos x)^2 + (sin x)^2 = 1.[/QUOTE]
It's the same base identity, so any way you want to write it is fine. I prefer to take more steps. Helps me keep straight what I'm doing. Guards me against the little errors I make.
 
Were almost about to do the shit your doing right now, were doing the Circle where 360 degrees = 2pie.

And i'm going to use this...
 
[quote name='ph33r m3']Were almost about to do the shit your doing right now, were doing the Circle where 360 degrees = 2pie.

And i'm going to use this...[/QUOTE]
I was helping out someone else with precalc today. Seeing degrees again was a trip, because they don't really come up after you learn to use radians. Stupid crappy degrees...
 
[quote name='ph33r m3']Were almost about to do the shit your doing right now, were doing the Circle where 360 degrees = 2pie.

And i'm going to use this...[/quote]

yea, in about 2 or 3 weeks, you will need this :D

haha...when are we gonna play street 3???

you're always on splinter cell and never leave
 
[quote name='jmcc']I was helping out someone else with precalc today. Seeing degrees again was a trip, because they don't really come up after you learn to use radians. Stupid crappy degrees...[/quote]

yea, my teacher is trying to deviate away from degrees into radians and pi radians...thanks for the help, jmcc...he doesnt collect homework, but when we went over it in class today, nobody got more than 4 of the questions (out of 9) except for me (with your help ;)) i got 5 on my own and the 2 you helped me with...so i only needed help with 2 more

thanks again! :D
 
[quote name='swetooth9']yea, in about 2 or 3 weeks, you will need this :D

haha...when are we gonna play street 3???

you're always on splinter cell and never leave[/quote]

Sorry bro, definitely soon, but I got grounded for coming home late past my curfew so it might be a while.

I've always asked my teachers "when am I going to use this? Why next year!" That's always the answer I get.

I'm barely getting an A in Pre-Cal not fun. Oh ok, here we go, the tan x = sinx/cosx, see that thing we taught you Tangent = Opposite/Adjacent! Screw that! It's now sin/cos!!!!

I hate also when lets say 45 degrees is root 2 over 2 or something, shit's reeeeetarded.
 
[quote name='ph33r m3']Sorry bro, definitely soon, but I got grounded for coming home late past my curfew so it might be a while.

I've always asked my teachers "when am I going to use this? Why next year!" That's always the answer I get.

I'm barely getting an A in Pre-Cal not fun. Oh ok, here we go, the tan x = sinx/cosx, see that thing we taught you Tangent = Opposite/Adjacent! Screw that! It's now sin/cos!!!!

I hate also when lets say 45 degrees is root 2 over 2 or something, shit's reeeeetarded.[/QUOTE]
SOH-CAH-TOA will help you a lot.

And if you're going to become an engineer or any science, you'll definitely be using these things later.
 
so far the only math i've really used in the real world was geometry. i had a job a few years back injecting urethane foam insulation into panels for walk-in coolers. to calculate the amount of foam needed you had to enter the base-height-width measurements into the computer, but we had some odd shapes sometimes (trianlges, trapezoids, and multi-sided irregular shapes). i seemed to be the only guy in my dept that knew how to measure the shapes properly.

there's a little math involved in cinematography, but nothing complicated so far. i'm sure you'll need math if you do anything financial or scientific, but otherwise just knowing how to balance a checkbook seems to be the most math intensive activity for the average person.
 
[quote name='beerguy961']any science, you'll definitely be using these things later.[/quote]

yea, i'm lookin into science...
 
[quote name='beerguy961']SOH-CAH-TOA will help you a lot.

And if you're going to become an engineer or any science, you'll definitely be using these things later.[/quote]

Yeah i know that SOH CAH TOA stuff, it's easy.

In Chemistry I really haven't used radians or degrees funny enough, being in Biology, Physics, and Chemistry and next year not taking a science I haven't used much math.

I guess Stoicheimoetrey is where it gets tricky but that's simple math.
 
[quote name='Gregory Kimball']I would have been able to answer a couple months ago, but that was last semester. My brain can only handle so much math, and right now it's on matrices.

Good luck.[/QUOTE]

I hope you don't take analytical geometry and calculus. You have to know your trig, your geometry and algebra, and the calculus which my instructor says "ties it all together".
 
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