Solving a Trigonometric Equation

[alane1994]

I have this as part of a calculus problem. I guess I am a little rusty on this. Any help would be appreciated.

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$$4\cos^2{x}=\frac{\sec^2{x}}{4}$$

I believe that I need to solve for cosx. And then determine what cosx is in radians. That should be the lower limit of the integration. I know how it should work... it is just the process...

 

[tkhunny]

re: Solving a Trignometric Equation

Since you brought up the rust, perhaps we can start with that.

Do you know that cos(x) = 1/sec(x)?

 

[alane1994]

re: Solving a Trignometric Equation

I know most of the basic ones...

 

[alane1994]

re: Solving a Trignometric Equation

Also, I suppose I should give some background on what I am doing. I am finding the area between curves. The trig functions on either side of the = are the two curves.

 

[Fantini]

re: Solving a Trignometric Equation

Well, the full list would be:

$$\begin{cases}
\sec x = \frac{1}{\cos x}, \\
\csc x = \frac{1}{\sin x}, \\
\cot x = \frac{1}{\tan x} = \frac{\cos x}{\sin x}.
\end{cases}$$

Therefore, $4 \cos^2 x = \frac{\sec^2 x}{4} = \frac{1}{4} \frac{1}{\cos^2 x}$, leading to $16 \cos^4 x = 1$.

Try to go from here. :D

 

[alane1994]

re: Solving a Trignometric Equation

would it be
$$x= \frac{\pi}{3},\frac{2\pi}{3}$$

 

[Jameson]

re: Solving a Trignometric Equation

would it be
$$x= \frac{\pi}{3},\frac{2\pi}{3}$$

Those are both solutions yes, but there are infinitely more depending on the domain in question. If the domain is $[0,\pi]$ then those are the only two solutions.

 

[alane1994]

re: Solving a Trignometric Equation

I got the answer wrong...

 

[Jameson]

re: Solving a Trignometric Equation

I got the answer wrong...

Well Mathematica agrees with that answer on that domain. You mentioned that this wasn't the whole problem so without further info I don't know what to tell you.

Also, keep in mind that we can't help you with homework that is graded unless your professor is ok with you receiving any guidance so be careful with this.

 

[alane1994]

re: Solving a Trignometric Equation

It is indeed graded, but he encourages guidance. Just as long as people are helping you get the answers, not giving them to you. We have an academic center with professors who's entire job consists of helping students with homework questions.

 

[Fantini]

re: Solving a Trignometric Equation

With Jameson's comment in mind, perhaps this could be solved by posing the question in full. (Nod)

 

[alane1994]

re: Solving a Trignometric Equation

OK.
I will have to do this in the Calculus section.