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- Thread starter Elissa89
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- Mar 5, 2012

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I'm assuming you mean $\sec^3(\theta)-2=0$?Before I post the question I need to vent. I've about had it with my math professor. He isn't showing us how to solve problems that keep popping up in the math homework and I am 100% lost most of the time. Ok I'm done.

The question is

sec 3(theta)-2=0

If so, we can rewrite it as:

$$\sec^3(\theta)=2 \quad\Rightarrow\quad \sec\theta =\sqrt[3]2$$

can't we?

Oh, and can you say what $\sec$ actually is?

Usually we try to express formulas in $\cos$ and $\sin$ after all, which I think makes the analysis a bit easier.

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The secant is not cubed, it's sec 3*(theta)I'm assuming you mean $\sec^3(\theta)-2=0$?

If so, we can rewrite it as:

$$\sec^3(\theta)=2 \quad\Rightarrow\quad \sec\theta =\sqrt[3]2$$

can't we?

Oh, and can you say what $\sec$ actually is?

Usually we try to express formulas in $\cos$ and $\sin$ after all, which I think makes the analysis a bit easier.

- Jan 30, 2012

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If you have an opportunity, go to the office hour and let the professor know you concerns.Before I post the question I need to vent. I've about had it with my math professor. He isn't showing us how to solve problems that keep popping up in the math homework and I am 100% lost most of the time.

This can be parsed in many ways: \(\displaystyle \sec(3\theta)-2=0\), \(\displaystyle \sec(3\theta-2)=0\), perhaps even \(\displaystyle \sec(3\theta)^{-2}=0\) or \(\displaystyle s\cdot e\cdot c\cdot 3(\theta)-2=0\) where $3$ is some function of $\theta$ (why else would you use parentheses around $\theta$ and not the argument of $\sec$?). Also, the problem may ask you to solve the equation, to prove that it has no solutions, to plot the solutions, to prove that solutions are not expressible in radicals or many other things. All this must be in the problem statement.sec 3(theta)-2=0

If you need to solve the equation $\sec(3\theta)-2=0$, then you can proceed as follows.

\(\displaystyle \begin{align}

\sec(3\theta)-2=0&\iff\sec(3\theta)=2\\

&\iff\dfrac{1}{\cos(3\theta)}=2\\

&\iff\cos(3\theta)=\dfrac12\\

&\iff 3\theta=\pm\dfrac\pi3+2\pi k,k\in\mathbb{Z}\\

&\iff\theta=\pm\dfrac\pi9+\dfrac23\pi k,k\in\mathbb{Z}

\end{align}\)

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Ummm... thanks but can you fix this so I can read it more easily?If you have an opportunity, go to the office hour and let the professor know you concerns.

This can be parsed in many ways: \(\displaystyle \sec(3\theta)-2=0\), \(\displaystyle \sec(3\theta-2)=0\), perhaps even \(\displaystyle \sec(3\theta)^{-2}=0\) or \(\displaystyle s\cdot e\cdot c\cdot 3(\theta)-2=0\) where $3$ is some function of $\theta$ (why else would you use parentheses around $\theta$ and not the argument of $\sec$?). Also, the problem may ask you to solve the equation, to prove that it has no solutions, to plot the solutions, to prove that solutions are not expressible in radicals or many other things. All this must be in the problem statement.

If you need to solve the equation $\sec(3\theta)-2=0$, then you can proceed as follows.

\(\displaystyle \begin{align}

\sec(3\theta)-2=0&\iff\sec(3\theta)=2\\

&\iff\dfrac{1}{\cos(3\theta)}=2\\

&\iff\cos(3\theta)=\dfrac12\\

&\iff 3\theta=\pm\dfrac\pi3+2\pi k,k\in\mathbb{Z}\\

&\iff\theta=\pm\dfrac\pi9+\dfrac23\pi k,k\in\mathbb{Z}

\end{align}\)

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Are you using a mobile device?Ummm... thanks but can you fix this so I can read it more easily?

- Jan 30, 2012

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- Mar 5, 2012

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Are you using a mobile device?

Interestingly the problems that we used to have on rendering formulas on mobiles devices seem to have disappeared.

Either way, the formulas that Evgeny posted show up just fine on my mobile device.

I did notice that his original post did not render, but this has been fixed, and the response of the OP actually shows the fixed rendering.

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It appears that Evgeny's post was quoted after he wrapped his code in math tags. I wasn't aware though that the issue of inline LaTeX bleeding into surrounding text on some mobile devices had gone away. That was the only thing I could think of that would make his otherwise nicely formatted post not be easily read.Interestingly the problems that we used to have on rendering formulas on mobiles devices seem to have disappeared.

Either way, the formulas that Evgeny posted show up just fine on my mobile device.

I did notice that his original post did not render, but this has been fixed, and the response of the OP actually shows the fixed rendering.

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- Feb 5, 2013

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List of trigonometric identities.

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Ok, I get how you solved it, however when I input it the computer tells me it's wrong.Ummm... thanks but can you fix this so I can read it more easily?

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- Mar 5, 2012

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What did you try to input?Ok, I get how you solved it, however when I input it the computer tells me it's wrong.

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- #13

Ok I figured it out, I had to include 5*pi/9 +2/3*pi*kWhat did you try to input?

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- Mar 5, 2012

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For the record, that is only half of the solution.Ok I figured it out, I had to include 5*pi/9 +2/3*pi*k

The full solution is 5*pi/9 +2/3*pi*k (or -pi/9 +2/3*pi*k) combined with pi/9 +2/3*pi*k.

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I know, I included bothFor the record, that is only half of the solution.

The full solution is 5*pi/9 +2/3*pi*k (or -pi/9 +2/3*pi*k) combined with pi/9 +2/3*pi*k.

- Jan 30, 2018

- 368

When I was teaching Calculus I had the practice of starting each class by asking if there were any questions about the homework and going over any problems asked about. I also put two or three homework problems on the tests as well as some problems that were just simple variations of those and one or two that were completely different but used the concepts the students should have learned.Before I post the question I need to vent. I've about had it with my math professor. He isn't showing us how to solve problems that keep popping up in the math homework and I am 100% lost most of the time. Ok I'm done.

The question is

sec 3(theta)-2=0

One time a student complained bitterly that I had never taught them how to solve this kind of problem. I thought it would be one of those that "were completely different but used the concepts the students should have learned". When I looked at it, it was, in fact, one of the homework problems assigned. It was one that I had gone over in class, and I was able to open the student's notebook and show where he had that specific problem completely solved!

So students (and this was a good student who got a good grade in the course) do not always remember exactly what their teacher has gone over in class!