Another stupid math question

[rockytriton]

Ok, I'm really having problems understanding using fractions and radicals. :confused:

 

I know that:

 

sin(PI/6) = 1/2

cos(PI/6) = sqr(3)/2

 

but the book that I have says that:

 

tan(PI/6) = sqr(3)/3

 

I don't understand this, wouldn't the tangent be 1/2 divided by sqr(3)/2? That should be 1/2 times 2/sqr(3), cancel out the 2s and you get 1/sqr(3). Where is my math going wrong here?

[Erasmus00]

I don't understand this, wouldn't the tangent be 1/2 divided by sqr(3)/2? That should be 1/2 times 2/sqr(3), cancel out the 2s and you get 1/sqr(3). Where is my math going wrong here?

 

1/sqrt3 *sqrt3/sqrt3 = sqrt3/3.

 

Usually, fractions aren't considered "simplified" untill you've put the roots in the numerator.

-Will

[pgrmdave]

You're right, they simply multiply by 1 or sqr(3)/sqr(3) so they have

 

tan(PI/6) = sin(PI/6) / cos(PI/6)

tan(PI/6) = (1/2) / (sqr(3) / 2)

tan(PI/6) = 1 / sqr(3)

tan(PI/6) = ( 1 / sqr(3) )* ( sqr(3) / sqr(3) )

tan(PI/6) = ( 1 * sqr(3) ) / ( sqr(3) ^ 2 )

tan(PI/6) = sqr(3) / 3

[rockytriton]

great, I understand now. Thanks for clearing that up guys! I didn't realize that it wasn't considered simplified until the roots are in the numerator.

[Bo]

the reason for this is actually quite simple: sqrt's are annoying and denominators are annoying; so you shouldn't combine them....

 

Bo

[cwes99_03]

HEHEHEHE, never heard it that way.

 

Simplification by definition is to get the simplest form in the denominator. In this case, a whole number is simpler than a radical.