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`(sin^2theta)/(1+cos theta)=1` What are the values of `theta` in the interval below...

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jgeertz | College Teacher | (Level 1) Associate Educator

Posted March 3, 2013 at 10:17 PM via web

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`(sin^2theta)/(1+cos theta)=1`

What are the values of `theta` in the interval below that satisfy the equation?



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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted March 3, 2013 at 11:57 PM (Answer #1)

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Solve `(sin^2theta)/(1+costheta)=1` for `0<=theta<=360^@` :


`sin^2theta=1+costheta` Use the Pythagorean relationship





`costheta=-1==>theta=180^@` but this is extraneous -- the fraction is undefined at `theta=180^@`


The solutions are `theta=90^@,270^@`


The graph of `y=(sin^2theta)/(1+costheta)` and y=1:

**The graph is in radians so `theta=pi/2,(3pi)/2` **

*** Sorry about the costhheta -- it will not let me correct them. Hover over them and you will see that they are typed in correctly.

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chainrule | (Level 1) eNoter

Posted March 5, 2013 at 11:46 AM (Answer #2)

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It is better to use radians instead of degrees for such a question.

The domain is 0 to Pi inclusive.


Substituting (Cosx)^2+(Sinx)^2 for 1.


Solving for zero, and canceling like terms.


Factoring out the cosx's


Where each seperate factor of the formula have to equal zero to get our desired solutions.

They turn out to be: Pi/2 and Pi


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