Trig Problem

cuervo72 · 03-13-2012, 10:48 AM

Saw this problem posted on FB and began working on it, but it looks like it was resolved by someone but I didn't see the answer (was shared a number of times so I was basically a lurker thrice removed). My trig is rusty (it's been 20 years) so I'm not sure if I'd arrive at an answer, but it bugging the heck out of me. Any takers?

Simplify to single integer or single trig function:

1 + csc^2 Θ
------------------
1 + cot Θ

Rules:
sin^2 + cos^2 = 1
1 + tan^2 = sec^2
1 + cot^2 = csc^2

csc = 1/sin
cos = 1/sec
tan = 1/cot
tan = sin/cos
cot = cos/sin

jbergey22 · 03-13-2012, 10:49 AM

I suddenly feel really dumb

Rizon · 03-13-2012, 10:51 AM

Quote:

Originally Posted by jbergey22

I suddenly feel really dumb

My guess is either ^_^ or ~(_8(o)

Honolulu_Blue · 03-13-2012, 10:51 AM

Leave Sarah Palin's family alone!

sterlingice · 03-13-2012, 11:39 AM

I'm going to ask my really dumb question for the day here:

Is csc^2 Θ = (csc Θ) * (csc Θ)?

Trig I could never visualize like algebra so stuff like that threw me from time to time.

SI

cuervo72 · 03-13-2012, 11:51 AM

Yes, ^2 denotes square.

Logan · 03-13-2012, 12:38 PM

Any trig is a problem.

DaddyTorgo · 03-13-2012, 12:39 PM

Ouch. My head hurts. Damn middle-school math.

britrock88 · 03-13-2012, 07:38 PM

If that simplifies to something easy, the solver is doing it wrong.

(It ALMOST simplifies to (2*cot Θ) or (2 + cot Θ), but either of these solutions relies on an algebraic misstep.)

britrock88 · 03-13-2012, 07:42 PM

Yeah, Wolfram Alpha can't simplify it, either.

rowech · 03-13-2012, 07:48 PM

Quote:

Originally Posted by britrock88

If that simplifies to something easy, the solver is doing it wrong.

(It ALMOST simplifies to (2*cot Θ) or (2 + cot Θ), but either of these solutions relies on an algebraic misstep.)

Agreed. I spent 20 minutes or so on it and I can't find it.

fantom1979 · 03-13-2012, 08:41 PM

At my age, it is just easier to climb a tree and run a tape measure down it than it is to do trig.

Vince, Pt. II · 03-13-2012, 09:02 PM

Quote:

Originally Posted by britrock88

If that simplifies to something easy, the solver is doing it wrong.

(It ALMOST simplifies to (2*cot Θ) or (2 + cot Θ), but either of these solutions relies on an algebraic misstep.)

Yup, I got this and then realized I must have made a mistake.

CrimsonFox · 03-13-2012, 09:05 PM

Quote:

Originally Posted by Rizon

My guess is either ^_^ or ~(_8(o)

Rizon are you making penises again? What is that?

cuervo72 · 03-13-2012, 09:57 PM

Good, so maybe I'm not that far gone then. I think I'd have come up with something if it was cot^2 in the denominator, but as-is I kept going around in circles.

Someone said they had a solution for it though (but posted somewhere besides where I saw the question, and three friends removed I wasn't going to ask) so who knows.

sterlingice · 03-13-2012, 10:20 PM

This has to be one of those where you multiply top or bottom by 1-(blah) to get 1-(blah)^2 to simplify something out. But I wasn't seeing it in the 5 minutes at lunch before I realized I needed to pick in Fantasy Baseball or the 10 minutes before I go to bed. I should probably pick better times to tackle it.

SI

Passacaglia · 03-15-2012, 10:25 AM

Quote:

Originally Posted by britrock88

If that simplifies to something easy, the solver is doing it wrong.

(It ALMOST simplifies to (2*cot Θ) or (2 + cot Θ), but either of these solutions relies on an algebraic misstep.)

Pretty much the same here. I can almost get it to (1 - cot Θ), but the 1 in the numerator screws it up for me.

03-13-2012, 10:51 AM	#4
Honolulu_Blue Hockey Boy Join Date: Oct 2000 Location: Royal Oak, MI	Leave Sarah Palin's family alone! __________________ *Steve Yzerman*: 1,755 points in 1,514 regular season games. 185 points in 196 postseason games. A First-Team All-Star, Conn Smythe Trophy winner, Selke Trophy winner, Masterton Trophy winner, member of the Hockey Hall of Fame, Olympic gold medallist, and a three-time Stanley Cup Champion. Longest serving captain of one team in the history of the NHL (19 seasons).

03-13-2012, 11:39 AM	#5
sterlingice Hall Of Famer Join Date: Apr 2002 Location: Back in Houston!	I'm going to ask my really dumb question for the day here: Is csc^2 Θ = (csc Θ) * (csc Θ)? Trig I could never visualize like algebra so stuff like that threw me from time to time. SI __________________ Houston Hippopotami, III.3: 20th Anniversary Thread - All former HT players are encouraged to check it out! Janos: "Only America could produce an imbecile of your caliber!" Freakazoid: "That's because we make lots of things better than other people!"

03-13-2012, 11:51 AM	#6
cuervo72 Head Coach Join Date: Dec 2002 Location: Maryland	Yes, ^2 denotes square. __________________ null

03-13-2012, 07:38 PM	#9
britrock88 Pro Starter Join Date: Jan 2011 Location: Madison, WI	If that simplifies to something easy, the solver is doing it wrong. (It ALMOST simplifies to (2cot Θ) or (2 + cot Θ), but either of these solutions relies on an algebraic misstep.) Last edited by britrock88 : 03-13-2012 at 07:39 PM.*

03-13-2012, 09:57 PM	#15
cuervo72 Head Coach Join Date: Dec 2002 Location: Maryland	Good, so maybe I'm not that far gone then. I think I'd have come up with something if it was cot^2 in the denominator, but as-is I kept going around in circles. Someone said they had a solution for it though (but posted somewhere besides where I saw the question, and three friends removed I wasn't going to ask) so who knows. __________________ null

03-13-2012, 10:49 AM	#2
jbergey22 Grizzled Veteran Join Date: Nov 2006 Location: Minnesota	I suddenly feel really dumb

03-13-2012, 12:38 PM	#7
Logan Head Coach Join Date: Oct 2000 Location: NYC	Any trig is a problem.

03-13-2012, 12:39 PM	#8
DaddyTorgo Hall Of Famer Join Date: Oct 2002 Location: Massachusetts	Ouch. My head hurts. Damn middle-school math.

03-13-2012, 07:42 PM	#10
britrock88 Pro Starter Join Date: Jan 2011 Location: Madison, WI	Yeah, Wolfram Alpha can't simplify it, either.

03-13-2012, 08:41 PM	#12
fantom1979 College Benchwarmer Join Date: Apr 2008 Location: Sterling Heights, Mi	At my age, it is just easier to climb a tree and run a tape measure down it than it is to do trig.

03-13-2012, 10:20 PM	#16
sterlingice Hall Of Famer Join Date: Apr 2002 Location: Back in Houston!	This has to be one of those where you multiply top or bottom by 1-(blah) to get 1-(blah)^2 to simplify something out. But I wasn't seeing it in the 5 minutes at lunch before I realized I needed to pick in Fantasy Baseball or the 10 minutes before I go to bed. I should probably pick better times to tackle it. SI __________________ Houston Hippopotami, III.3: 20th Anniversary Thread - All former HT players are encouraged to check it out! Janos: "Only America could produce an imbecile of your caliber!" Freakazoid: "That's because we make lots of things better than other people!"

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