Solving an Equation with Cosine

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Homework Help Overview

The discussion revolves around solving an equation involving cosine, specifically the relationship between the variables x, r, and the angle a. The original poster presents a scenario where x and r are known values, leading to a derived equation that appears to yield a negative result for cos^2(a).

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to manipulate the equation involving cos^2(a) but encounters difficulties when the derived value suggests an impossible scenario for cosine. Some participants question the validity of the original equation and the implications of obtaining a negative value for cos^2(a).

Discussion Status

Participants are exploring the implications of the mathematical relationships presented. There is acknowledgment of a misunderstanding regarding the equation's setup, and some guidance has been offered regarding the correct interpretation of the cosine identity. The discussion reflects a mix of attempts to clarify the problem and address potential misinterpretations.

Contextual Notes

The original poster expresses confusion over the results derived from the equation, particularly in relation to the expected angle provided by a textbook. There is an indication of misinterpretation of the solution process, which has led to further exploration of the problem's assumptions.

salman213
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1.x = rcos(a)cos(a)

x is known
r is known

I can't seem to get this!

x = -2
r = 7

therefore

-2/7 = cos(a)*cos(a)

so..

-2/7 = cos^2(a)

i know cos^2(a) = 1 + cos2a / 2

-2/7 = 1 + cos2a / 2

so
-4/7 -1 = cos2a

I cannot take cos inverse of this value since it is "greater" than 1 (-1.57)

the book says the angle is 106.6 degrees!

HELP!



Homework Equations





The Attempt at a Solution

 
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Here's your problem right here:

salman213 said:

i know cos^2(a) = 1 + cos2a / 2


Nope, it's [itex]\cos^2(a)=(1+\cos(2a))/2[/itex]. Both terms are divided by 2.
 
yea sorry that's what i meant

but it still doesn't work out..
 
Egad, you have an even more serious problem that I missed.

salman213 said:
-2/7 = cos(a)*cos(a)

You can't square cos(a) and get a negative number. This equation has no solution in the real numbers.
 
Who is Egad?EDITED!

NEVERMIND I figured it out, i was interpreting the solution incorrectly...

Thanks anyways!
 
salman213 said:
Who is Egad?

:smile: "egad" is an exclamation like "crikey" or "blimey".
 

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