Graphs: A Better Way to Memorize Pi Fractions?

[CrossFit415]

Couldnt we just use whole numbers to graph on the x-axis instead of labeling them pi/2, pi, 3pi/2 ? Because it gets confusing having to memorize which pi fraction goes in order. Is there a better way to memorize these? Thanks

 

[LCKurtz]

Couldnt we just use whole numbers to graph on the x-axis instead of labeling them pi/2, pi, 3pi/2 ? Because it gets confusing having to memorize which pi fraction goes in order. Is there a better way to memorize these? Thanks

Do you mean like using degrees on the x-axis instead of radians? So the period of the sine function would be 360 and all the angles you mention above are nice whole numbers like 90, 180, and 270.

The answer is yes, we could do that. But if you think dealing with pi as you have mentioned above is a nuisance now, it is nothing compared with the nuisance you would encounter in calculus if you use degrees. The derivatives of sine and cosine functions work out the simplest when their argument is measured in radians. If you use degrees, all the formulas would have a nuisance factor compensating for that awkward choice. It is a similar situation that causes the natural logarithms (base e) to be the easiest to work with. If you haven't had calculus yet, you will have to wait to understand this, but you will see then.

 

[CrossFit415]

Do you mean like using degrees on the x-axis instead of radians? So the period of the sine function would be 360 and all the angles you mention above are nice whole numbers like 90, 180, and 270.

The answer is yes, we could do that. But if you think dealing with pi as you have mentioned above is a nuisance now, it is nothing compared with the nuisance you would encounter in calculus if you use degrees. The derivatives of sine and cosine functions work out the simplest when their argument is measured in radians. If you use degrees, all the formulas would have a nuisance factor compensating for that awkward choice. It is a similar situation that causes the natural logarithms (base e) to be the easiest to work with. If you haven't had calculus yet, you will have to wait to understand this, but you will see then.

I see. Hey thanks alot. I didn't know that degrees would complicate the whole process later on. But how would I memorize the pi fractions in order from x=0. I know that 45° = pi/4, 60° = pi/3 and 30° = pi/6. But the fractions that confuse me are the numbers front of pi such as 3pi/2, or 5pi/2 or 3pi/8.

 

[CrossFit415]

Actually I think I got it now. I could always convert them into degrees and plot them on the x-axis then just write them down as radians. I didn't think about that. Thanks alot.

 

[Mentallic]

A lot of students that are just being introduced to trig functions start to stress about this sort of thing. But trust me when I say it'll be a short-lived stress if you practice early on. No one expects you to memorize the sine of certain angles off by heart, because there are much easier methods to quickly determine it.
4 years after studying what you've presented here and I still imagine the 30^o 60^o 90^o triangle in order to find what sin(30^o) is for example.

 

[mharten1]

Just convert the radians to a common denominator if you can't determine which order to graph them in.

Of course you can graph trig functions with whatever numbers you want. 1 radian, 1 degree, etc. But it's easier to graph in radians, and usually you graph in known values. 1 radian is not a known value, but pi/2 radians is.

 

[Mentallic]

Just to clarify what mharten said about conversions, you can always start with \pi^c=180^o where ^c means radians (but isn't commonly used)

so if you want to find what 5\pi/4 is in degrees, then you multiply both sides by 5/4, so you get (5/4)\pi ^c=(5/4)\cdot 180^o=225^o

 

[CrossFit415]

Thanks a lot!