# i need help with pre-calculus

Discussion in 'ten-forward' started by WSFuser, Feb 19, 2006.

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1. ### WSFuserRegistered Member

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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.

2. ### aka:snowmanFormer Poster

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Last edited: Feb 19, 2006
3. ### big edRegistered Member

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The answer is "Q"! Trust me!!

4. ### WSFuserRegistered Member

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

5. ### aka:snowmanFormer Poster

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6. ### ~*Nat*~Registered Member

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7. ### snowboundRetired Moderator

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8. ### WSFuserRegistered Member

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i dont want to register

9. ### WSFuserRegistered Member

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with help from another forum, i got this far:

2 / 1.54 = sin² Θ + 2sin² Θ

10. ### BlueZannettiRegistered Member

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Not quite..., I'd find another source.

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

Blue

11. ### WSFuserRegistered Member

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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

12. ### MarjaHonestly, I'm not a bot!!

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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.......

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

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

Marja

13. ### BlueZannettiRegistered Member

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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

14. ### WSFuserRegistered Member

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d'oh, i missed that. thanx for the help tho

15. ### CochiseA missed friend

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

Cochise, Tootin' Carmen in Carmel...

16. ### SpikeyBRegistered Member

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

17. ### WSFuserRegistered Member

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it doesnt matter cuz theta is a greek letter not egyptian
the two 1.54 cancel out to give one as the denominator

18. ### SpikeyBRegistered Member

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That would be the case if the rhs of the equation was:

1.54((1 - cos Θ) + 2sin² Θ)

19. ### probprinceRegistered Member

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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.

20. ### ~*Nat*~Registered Member

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21. ### FirecatRegistered Member

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

22. ### sweaterRegistered Member

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[MOVE]I hate math!!![/MOVE]

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

23. ### NAMORRegistered Member

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

24. ### WSFuserRegistered Member

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

25. ### PrimroseRegistered Member

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

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/