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

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

`0<=theta<=360`

 

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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

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

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

`1-cos^2theta=1+costheta`

`cos^2theta+costheta=0`

`costheta(costheta+1)=0`

`costheta=0==>theta=90^@,270^@`

`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.

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial