Solving for the Variable in Curves Intersection

[leroyjenkens]

Homework Statement

So what I've been doing to solve these questions is to set the two equations of the curves equal to each other and solving for the variable, which gives me the points where they intersect. But I'm having problems solving for the variable in some of these.

For example (sec^2)/2 is the top of the curve and 2cos^(2)x is the bottom curve. I want to set them both equal to each other to find where they meet, but I have no idea how to solve for that variable.

Wow, the latex was working, and when I edited, it stopped working.

The Attempt at a Solution

I tried setting them equal to each other and multiplying both sides by 2 to get rid of the fraction. But then I still have a cosine and a secant. I tried turning the cosine into a secant, but that just gave me a fraction again and another problem to deal with.

Thanks.

 

[ArcanaNoir]

The latex doesn't show after you edit until you refresh.

after you multiply by 2, take the square root of both sides. Then see if you can continue.

 

[eumyang]

Wow, the latex was working, and when I edited, it stopped working.

After you edit, if the LaTeX isn't working, try hitting refresh (F5).

I tried setting them equal to each other and multiplying both sides by 2 to get rid of the fraction. But then I still have a cosine and a secant. I tried turning the cosine into a secant, but that just gave me a fraction again and another problem to deal with.

From here, try multiplying both sides by cos² x. That will get rid of the fraction.