# Turning pie & sqrt into.

1. Nov 21, 2007

### JasonKit

Turning pie & sqrt into.......

I am desperately need help how to turn pie and sqrt to fraction?

Here is my question, punch in sin(pi/4) and the answer would be .7071067812
I know how to use fraction mode i'm no noob. I tried that feature and it didn't works.
Any brilliant idea would be appreciated!

2. Nov 21, 2007

### stewartcs

Cherry pie or apple? :rofl:

Just kidding, pi is an irrational number, i.e. there is no fraction equivalent, only an approximation to a certain decimal place.

Square root is a function not a number.

3. Nov 21, 2007

### JasonKit

In fact,

it can be turn to fraction, friend of mine, show it to me and I forgot how to do it, o let me see how long is been 2 YEARS AGO. If you have any genius idea please help me out not intimidated me.:grumpy:

If you know this that .7071067812 is equal to sqrt 2/2.

I just need help how decimal turn it to fraction
Let me give you another example:

sin(pi/3)= .8660254038

what is the fraction for this?

Last edited: Nov 21, 2007
4. Nov 21, 2007

### stewartcs

Your friend was wrong. Again, Pi is an irrational number.

http://en.wikipedia.org/wiki/Π

5. Nov 21, 2007

### JasonKit

are you even trying the problem that I provide above?

6. Nov 21, 2007

### stewartcs

So your question is not what is the fraction equivalent of Pi, but rather what is the fraction equivalent of sin(pi/3). Two different things.

All you need is the Unit Circle. See attached...

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7. Nov 21, 2007

### stewartcs

8. Nov 21, 2007

### JasonKit

it helps a little bit, I do know this unit circle and I even memorize it.- However I still need to know how to do it on the calculator which ti-83 plus.

9. Nov 21, 2007

### stewartcs

The ANS-->FRAC function on a TI-83 Plus won't give you the fractional equivalent of that. It's beyond its capabilities. The Voyager 200 (and possibly the TI-89) will though.

10. Nov 21, 2007

### JasonKit

Thanks for the look out, I'll find a way. I did it once, i just forgot which feature it does that.

11. Nov 21, 2007

### dodo

If sin(pi/3) is approximately .8660254038, then it is obviously (and again, approximately) equal to the fraction 8660254038/10000000000. Now you can try to reduce this fraction, for example by looking for the unique prime factors of 8,660,254,038 and 10,000,000,000 and cancelling the common ones; or, which is the same thing, by dividing 8,660,254,038 and 10,000,000,000 by its g.c.d. (in the ti-83, this is math-num-9:gcd). Since gcd (8660254038 ,10000000000) = 2, and 8660254038 / 2 = 4330127019, and 10000000000 / 2 = 5000000000, the number .8660254038 equals the fraction 4330127019/5000000000.

But notice three things:
1) .8660254038 equals the fraction 4330127019/5000000000, but none of them equals sin(pi/3). Both of them only approximate sin(pi/3), up to a certain numbers of decimals. With less decimals, the approximation would have been 8/10, or 86/100, or 866/1000, or ...
2) Everything they have been telling you is true; these numbers are irrationals, and you can only approximate them with a fraction. On the other hand, if what you wanted was to convert a given decimal like .8660254038 to a fraction, that can be done as above, but has nothing to do with sin(pi/3), except as an approximation.
3) Of course this is just a guess of what you want, because you are not explaining yourself very well, and by repeating "it can be done" the question doesn't get any clearer.

12. Nov 21, 2007

### Ben Niehoff

This sort of thing is why calculators should be banned in math classes...

Jason, your calculator can't convert the decimal representation to a fraction, because sin(pi/3) is not a rational number.

$$\sin \frac{\pi}{3} = \frac{\sqrt 3}{2}$$

13. Nov 21, 2007

### JasonKit

Thanks for all your help, I lost contact with my friend, he is the one who show me the trick on ti-83 plus. I saw it and he taught me that. Its been awhile.

14. Nov 21, 2007

### Ben Niehoff

There might be an "exact mode" or something like that. It won't convert a decimal into "sqrt(3)/2", but it should give exact formulas for common sine and cosine values. Try asking on a TI-83 forum?

15. Nov 21, 2007

### gabee

If the angle is one of the most commonly used ones (i.e. the ones listed on the unit circle), you can do this.

Enter sin(pi/3)...the calculator will tell you it is 0.866025404.
Since you know that the common sine/cosine values are things that have a square root in the numerator, you might want to square the answer that the calculator gave you and see if it's something you recognize. For instance, take
(0.866025404)^2 = 0.75
which you recognize as 3/4. Since you squared it, now let's square root it to find
sqrt(3/4) = sqrt(3)/2
which I assume is the symbolic answer you're looking for.

Another similar trick you could use if you want to know the symbolic form of arcsin(0.866025404) = 1.04719755
Since I know the answer will likely have a factor of pi in the numerator, take
1.04719755/pi = 0.333333333
which you recognize as 1/3. So, 1.04719755 = pi/3.

Or you could just remember the unit circle!

16. Nov 21, 2007

### Office_Shredder

Staff Emeritus
This is actually pretty slick