i need help with pre-calculus

[WSFuser]

i have an equation:

x = 1.54(1 - cos Θ) + 2sin² Θ

I have to find an angle theta (Θ) between 0° and 360° that satifies the equation when x = 2. if anyone can help me that would be great.

[aka:snowman]

edit edit edit edit

[big ed]

-{ Quote: "i have an equation:

x = 1.54(1 - cos Θ) + 2sin² Θ

I have to find an angle theta (Θ) between 0° and 360° that satifies the equation when x = 2. if anyone can help me that would be great." }-

The answer is "Q"! Trust me!!

[WSFuser]

i need someone to show me how to simply the expression, not how to use a calculator.

[aka:snowman]

edit edit edit edit

[~*Nat*~]

Seeing all these strange signs.........



I think I'm getting a headache...... http://img459.imageshack.us/img459/2897/kotz8so.gif

[snowbound]

http://www.mathgoodies.com/forums/forum.asp?FORUM_ID=14


snowbound

[WSFuser]

-{ Quote: "http://www.mathgoodies.com/forums/forum.asp?FORUM_ID=14


snowbound" }-
i dont want to register

[WSFuser]

with help from another forum, i got this far:

2 / 1.54 = sin² Θ + 2sin² Θ

[BlueZannetti]

-{ Quote: "with help from another forum, i got this far:

2 / 1.54 = sin² Θ + 2sin² Θ" }-Not quite..., I'd find another source.

55.02349 degrees. Now show your work.....

Blue

[WSFuser]

-{ Quote: "Not quite..., I'd find another source.

55.02349 degrees. Now show your work.....

Blue" }-
2 = 1.54(1 - cos Θ) + 2sin² Θ

if i divide 1.54 from both sides i get

2 / 1.54 = (1 - cos Θ) + 2sin² Θ

then remembering that sin² Θ + cos² Θ = 1, i can substitute in sin² Θ for 1 - cos Θ.

2 / 1.54 = sin² Θ + 2sin² Θ

thats all i got

[Marja]

LOL! Hey Fuser, don't ya hate when they want to see 'how you got your answer'?

BlueZ must have said that or had it said to him, at some time......:)
(He said that pretty fast!)

Here is a help forum, if ya need more.......:D

http://www.artofproblemsolving.com/Forum/forum-66.html

Yes, DO show us your work when ya get 'it'! OK?;)


Marja8)

[BlueZannetti]

-{ Quote: "2 = 1.54(1 - cos Θ) + 2sin² Θ

if i divide 1.54 from both sides i get

2 / 1.54 = (1 - cos Θ) + 2sin² Θ

then remembering that sin² Θ + cos² Θ = 1, i can substitute in sin² Θ for 1 - cos Θ.

2 / 1.54 = sin² Θ + 2sin² Θ

thats all i got" }-You dropped a power.

sin² Θ + cos² Θ = 1, rearranging, sin² Θ = 1 - cos² Θ, not 1 - cos Θ.

You're on the right conceptual track though, so you're most of the way there. Get the equation in terms of one of the transcendental functions, but you really should look at substituting that sin² Θ term with (1 - cos² Θ), that yields a simple quadratic in cos Θ. Make the temporary variable transformation z = cos Θ and solve the quadratic for z. That solution has two branches, but only one is physically correct (i.e. shows the right bounding behaviour for cos Θ; that is, being in the bounded domain of -1 to 1).

Blue

[WSFuser]

-{ Quote: "You dropped a power.

sin² Θ + cos² Θ = 1, rearranging, sin² Θ = 1 - cos² Θ, not 1 - cos Θ." }-
d'oh, i missed that. thanx for the help tho

[Cochise]

I'd love to help but I know absolutely nothing about Egyptian Heiroglyphicals...


Cochise,8) Tootin' Carmen in Carmel...

[SpikeyB]

-{ Quote: "2 = 1.54(1 - cos Θ) + 2sin² Θ

if i divide 1.54 from both sides i get

2 / 1.54 = (1 - cos Θ) + 2sin² Θ" }-Shouldn't dividing both sides by 1.54 yield: 2 / 1.54 = (1 - cos Θ) + 2sin² Θ/1.54 ?

[WSFuser]

-{ Quote: "I'd love to help but I know absolutely nothing about Egyptian Heiroglyphicals...


Cochise, Tootin' Carmen in Carmel..." }-
it doesnt matter cuz theta is a greek letter not egyptian
-{ Quote: "Shouldn't dividing both sides by 1.54 yield: 2 / 1.54 = (1 - cos Θ) + 2sin² Θ/1.54 ?" }-
the two 1.54 cancel out to give one as the denominator

[SpikeyB]

-{ Quote: "the two 1.54 cancel out to give one as the denominator" }-That would be the case if the rhs of the equation was:

1.54((1 - cos Θ) + 2sin² Θ)

[probprince]

hey WSFuser

lol, yes, i remember the days of pre-calc. ok so i think here is how you do it:

you have 1.54 - 1.54cosӨ -2sin^2Ө = 2
ok, this reminds me of a quadratic equation, so we want to have a variable in place of cosӨ. However, we also have sinӨ in the equation. So, you can use one of the basic principles sin^2Ө +cos^2Ө = 1 and solve for sin^2Ө. you should get sin^2Ө = 1-cos^2Ө. but you have 2sin^2Ө in the equation, so your equivalent becomes 2-2cos^2Ө. plug this into the equation and everything becomes:

2cos^2Ө - 2 - 1.54cosӨ + 1.54 = 2
bring the two to the left side and substitute a temporary variable (such as a) for cosӨ and you will have a neat quadratic equation to use the quadratic formula:

2a^2 - 1.54a - 2.46 = 0

The rest is based on simple algebra and the quadratic equation. Check my work, i think the basic concept is correct though.
Hope this helped. ;)



edit: wow, i almost forgot, you have to substitute your variable back into the equation for a = cosӨ. you might have two answers (because of the quadratic equation) and check the validity of the solutions.

[~*Nat*~]

-{ Quote: "I'd love to help but I know absolutely nothing about Egyptian Heiroglyphicals..." }-





Me neither, cocheesy...me neither........


http://img135.imageshack.us/img135/9453/cleold6cd.jpg

http://bestsmileys.com/love2/16.gif

[Firecat]

Sigh.....I'd help but I know only the absolute basics of trigonometry right now. :(

[sweater]

-{ Quote: "i have an equation:

x = 1.54(1 - cos Θ) + 2sin² Θ

I have to find an angle theta (Θ) between 0° and 360° that satifies the equation when x = 2. if anyone can help me that would be great." }-

I hate math!!!>:(

But, maybe you have to ask some of our scientists here...like...ohh I don't like to name names. ;D

[NAMOR]

I'm so glad the only classes I have to take now are business ones.

[WSFuser]

i was able to confirm Blue's answer at another forum. anyways thanx all for ur help.

[Primrose]

When you get to DiffEq { DiffY'Q} (Differential Equations) next semester give me a buzz.:lurking:


A kid called up his Mom from his college and asked her for some money, because he was broke.

His Mother said, "Sure, sweetie. I will send you some money. You also left your calculus book here when you visited 2 weeks ago. Do you want me to send that up too?"

"Uhh, oh yeah, o.k." responded the kid.

So his Mom wrapped the book along with the checks up in a package, kissed Dad goodbye, and went to the post office to mail the money and the book. When she gets back, Dad asked, "Well how much did you give the boy this time?"

"Oh, I wrote 2 checks, one for $20, and the other for $1,000 out to him."

"That's $1020!!!" yelled Dad, "Are you crazy???"

"Don't worry hon," Mom said, kissed Dad on the on top of his bald head, "I taped the $20 check to the cover of his book, but I put the $1,000 one somewhere between the pages in chapter 19!"


Or you can DIY;)


http://www.sosmath.com/

[big ed]

-{ Quote: "When you get to DiffEq { DiffY'Q} (Differential Equations) next semester give me a buzz.:lurking:



Or you can DIY;)


http://www.sosmath.com/" }-

Yowza!! It's about time somebody acknowledged the power of "Q"!! It always works for mee!

Quantifying by leaps and bounds, Qute ed

[beetlejuice]

Shouldn't it read---

-{ Quote: "Yowza!! It's about time somebody acknowledged the power of "Q"!! It always works for mee!

Quantifying by leaps and bounds, Quazzy ed" }-

:blink: :wacko:

[WSFuser]

-{ Quote: "When you get to DiffEq { DiffY'Q} (Differential Equations) next semester give me a buzz.:lurking:" }-
will do. its good to know there members i can rely on for help with stuff other than computers.
-{ Quote: "A kid called up his Mom from his college and asked her for some money, because he was broke.

His Mother said, "Sure, sweetie. I will send you some money. You also left your calculus book here when you visited 2 weeks ago. Do you want me to send that up too?"

"Uhh, oh yeah, o.k." responded the kid.

So his Mom wrapped the book along with the checks up in a package, kissed Dad goodbye, and went to the post office to mail the money and the book. When she gets back, Dad asked, "Well how much did you give the boy this time?"

"Oh, I wrote 2 checks, one for $20, and the other for $1,000 out to him."

"That's $1020!!!" yelled Dad, "Are you crazy???"

"Don't worry hon," Mom said, kissed Dad on the on top of his bald head, "I taped the $20 check to the cover of his book, but I put the $1,000 one somewhere between the pages in chapter 19!"" }-
http://www.thedoors.ch/fun/smiley_rofl.gif
-{ Quote: "Or you can DIY;)


http://www.sosmath.com/" }-
thanx