# Mathematics -Tangent-

• 02-19-2005
xddxogm3
Mathematics -Tangent-
So you thought I was done with my mathematics questions. heheheh ;0)
my book doesn't have the answer, and wanted to know if i was correct.

Original Question:
Tan ((17*pi)/3)

Work:
((17*pi)/3)*(180/pi)=1020 degrees //convertion to degrees
1020 - 360 - 360 = 300 degrees
reference angle -60 -> sin (60) = -sqrt(3)/2 -> cos (60) = 1/2
Tan = sin/cos = (-sqrt(3)/2)*(2/1) = -sqrt(3)

Check:
Tan-1 (-sqrt(3)) ~ -1.0471975512
-1.0471975512 * (180/pi) = -60 degrees

Is this valid? I'm assuming yes.
Please, one of you wonderful smart math guru, provide me some input.
Thanks.
• 02-20-2005
SourceCode
Yes, looks correct.

Incase your curious, my horrible way of doing it goes like this, tell me if you understand it.

The problem: tan(17pi/3)

Notice that 2pi = 6pi/3 so 17pi/3 = 6pi/3 + 6pi/3 + 5pi/3, so we really want tan(5pi/3), and 5pi/3 is pi/3 less than 6pi/3 so it must be in the 4th quadrant and since tan(pi/3) = Sqrt(3) then tan(5pi/3) = -Sqrt(pi/3) since it is in the 4th quadrant.

That's how I think about it, probably not the best way lol. Your way of doing it is great.

Also if you ever get stuck and can't get help here, check out http://www.physicsforums.com/

They have awesome math subforums, I go there on a daily basis and read posts and stuff.
• 02-20-2005
Krak
ermmm...Calculator?;)

But 17pi/3 ~ 5.5 pi, which is, in theory, two whole circles, and some change, right? Would that just mean it's 360+360+whatever's left, and you take the tangent of THAT huge angle? Or do you dock off the 360's and take use the 'remainder' as the reference angle?

Some of that really doesn't seem to make a whole lot of sense to poor old Deany. You can't really apply such a huge angle to a triangle.
• 02-20-2005
PING
of course you cant apply such a huge angle to a triangle.. and its rite, you dock off the 360's. thats coz tan has a period of 2*pi that is, it repeats itself after an angle of 2*pi radians which is equal to 360 degrees
• 02-20-2005
xddxogm3
Source Code, you kick @\$\$.
Thanks for the info and the website
i'm just waiting for the registration process to finish on that site. it seems to be taking a while to receive the confirmation email.