Thread: Trigonometric Equation

So the questions asks find all the values of x in interval [0,2pi)

for the following equation

So the way I go about solving it is I subtract 12cos(x) to the other side and replace cos(2x) for the double angle identity which gives me:



So essentially, I distribute the 4 and rewrite the equation as follows:



Next I take out the common factor of 4 and factor out the whole equation:

to

After solving each one I get the following answers:

However, the online assignment guide is telling me I've gotten the wrong answers. I'm honestly lost, can anyone tell me where exactly I'm getting this wrong?

Originally Posted by dagbayani481

So the questions asks find all the values of x in interval [0,2pi)

for the following equation

So the way I go about solving it is I subtract 12cos(x) to the other side and replace cos(2x) for the double angle identity which gives me:



So essentially, I distribute the 4 and rewrite the equation as follows:



Next I take out the common factor of 4 and factor out the whole equation:

to

After solving each one I get the following answers:

However, the online assignment guide is telling me I've gotten the wrong answers. I'm honestly lost, can anyone tell me where exactly I'm getting this wrong?

I agree with your answers, but I honestly struggle to believe that they would give you a tough trigonometric equation with a common factor at the start - why have they just randomly taken something and multiplied it by 4? I suspect it could be an error in the question. What answers are you supposed to get? Is this the full question?

Originally Posted by Quacky

I agree with your answers, but I honestly struggle to believe that they would give you a tough trigonometric equation with a common factor at the start - why have they just randomly taken something and multiplied it by 4? I suspect it could be an error in the question. What answers are you supposed to get? Is this the full question?

I think the reasoning behind the equation is the fact that this is pre-calculus review in a calculus course. I'm assuming the difficulty of the problem is based on that fact. I'm starting to believe there might be an error in the question and I may bring it up to the instructor this Monday. Sadly, the problem does not provide an answer to the solution. In the meantime, I'm also posting a picture of the problem directly from the website to see if you guys can find any mistakes with my own solution:

Surely is a solution as well

Originally Posted by Prove It

Surely is a solution as well

Omg, facepalm. I could've sworn 2pi wasn't included in the interval. That's kind of dumb for them to include it considering 0 is basically the same as 2pi! Nonetheless, thank you for bringing that to my attention, I'll pay better attention to the problem next time

Originally Posted by dagbayani481

So the questions asks find all the values of x in interval [0,2pi) ...

according to the instructions, is not included in the interval

?

Originally Posted by skeeter

according to the instructions, is not included in the interval

?

Indeed. Yet on the screen shot in post #3 it's ....?