Radical Arithmetic and the Unit Circle

[Jason76]

These kinds of problems are killing me on homework. Causing me to be stuck for at least an hour on one problem:

\(\displaystyle \sin\dfrac{\pi}{3}(\cos\dfrac{\pi}{3}) - \tan\dfrac{\pi}{4}\)

\(\displaystyle \dfrac{\sqrt{3}}{2}(\dfrac{1}{2}) - 1\)

\(\displaystyle \dfrac{\sqrt{3}}{4} - 1\)

\(\displaystyle \dfrac{\sqrt{3}}{4} - \dfrac{4}{4}\)


Probably this answer will be wrong. Well actually I checked now and it was right.

The problem is the homework wants it reduced down to a certain level. For instance, it might want \(\displaystyle \dfrac{\sqrt{3}}{4} - \dfrac{4}{4}\) written as \(\displaystyle \dfrac{\sqrt{3} - 4}{4}\)or visa versa, and if it's not the way they want it, then it's wrong.

 

[lookagain]

Probably this answer will be wrong. Well actually I checked now and it was right.

The problem is the homework wants it reduced down to a certain level. For instance,

\(\displaystyle \dfrac{\sqrt{3}}{4} - 1\)*


it might want \(\displaystyle \dfrac{\sqrt{3}}{4} - \dfrac{4}{4}\) ** written as \(\displaystyle \dfrac{\sqrt{3} - 4}{4}\) *** or visa versa,

and if it's not the way they want it, then it's wrong.

You would never present it as **. That's an intermediate step between the alternate forms of \(\displaystyle \ \) * \(\displaystyle \ \) and\(\displaystyle \ \) ***.

You would give it as either * \(\displaystyle \ \) or \(\displaystyle \ \) ***.

 

[mmm4444bot]

stuck for at least an hour on one problem:

\(\displaystyle \sin\dfrac{\pi}{3}(\cos\dfrac{\pi}{3}) - \tan\dfrac{\pi}{4}\)

\(\displaystyle \dfrac{\sqrt{3}}{2}(\dfrac{1}{2}) - 1\)

\(\displaystyle \dfrac{\sqrt{3}}{4} - 1\)

\(\displaystyle \dfrac{\sqrt{3}}{4} - \dfrac{4}{4}\)

\(\displaystyle \dfrac{\sqrt{3} - 4}{4}\)

This looks okay; where are you stuck?

the homework wants it reduced down to a certain level

if it's not the way they want it, then it's wrong

Well, Jason, when a math course accepts only one form of an answer, they need to tell you in advance what that "certain level" of simplification is.

You did not post the instructions that came with the exercise. What exactly did they say?

(I hope this aspect is not where you were stuck for an hour...)

 

[Jason76]

This looks okay; where are you stuck?





Well, Jason, when a math course accepts only one form of an answer, they need to tell you in advance what that "certain level" of simplification is.

You did not post the instructions that came with the exercise. What exactly did they say?

(I hope this aspect is not where you were stuck for an hour...)

With a teacher you might get away with "almost simplifying", but with an online math program, they want one answer.

 

[mmm4444bot]

With a teacher you might get away with "almost simplifying", but with an online math program, they want one answer.

Yes, Jason. I understand what you're saying. This is why I told you that the course needs to provide you with the expected form (syntax) of your entry beforehand, especially if they only give you one shot and an incorrect entry changes your grade.

There is no rule in mathematics that defines sqrt(3)/4 - 1 to be more simple than [sqrt(3)-4]/4 -- or the other way around. In mathematics, we have a number of ways to rewrite expressions, and we choose to simplify to a specific form based on what we're going to do with the result. It's kinda like playing chess, in this regard. One thinks ahead, to upcoming steps, to see what the next manipulation ought to be.

Of course, in elementary exercises on simplifications themselves, there is no next step. I asked you what the instructions are for this particular exercise; I'm still assuming that they don't include any statements regarding the final result.

So, unless you've been told in advance which form the machine teacher has been programmed to accept, you just have to pick one; if you lose something worth worrying over -- because you picked "wrongly" -- then chat up your human contact, state what you entered, tell them that it is equivalent, and politely ask to be made whole.

Otherwise, try not to dwell on stuff like this too much. There will be times in your mathematics courses where things go awry due to misinformation of some sort, for reasons that are out of your control. Put things into perspective, and then pick your battles. :cool:

PS: A human grader might have dinged you a partial-point for writing 1 as 4/4, if you had actualy turned in that form, so lookagain's comment is worth remembering. Don't write 1 in rational form, in a simplified answer. Either of the other two forms are correct, 'till proven otherwise. Cheers