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Tan pi/8


Date: 03/16/2002 at 16:09:37
From: Stepheny
Subject: Calculus: trig functions

I must find the exact value of tan pi/8.
To do that I know I must use 

tan(alph - beta) = tan(alph) - tan(beta)/1 + tan(alph)tan(beta)

My problem is I can't find two angles alph and beta that I know the 
tan of (such as pi/4, pi/3, pi/6 angles) to equal pi/8.


Date: 03/16/2002 at 16:56:43
From: Doctor Jubal
Subject: Re: Calculus: trig functions

Hi Stepheny,

Thanks for writing Dr. Math.

You've thought of a good way to solve the problem, but you don't 
actually need two angles you know the tangents of. You only need one, 
if the other one is pi/8 itself. Let me elaborate.

Let's let alpha be pi/4, and beta be pi/8.  I assume you know 
tan(pi/4).

Then

                                  tan(pi/4) - tan(pi/8)
  tan(pi/4 - pi/8) = tan(pi/8) = ----------------------- 
                                  1 + tan(pi/4)tan(pi/8)

So now we have an equation with only one unknown quantity, tan(pi/8), 
to solve for.

Does this help?  Write back if you'd like to talk about this some
more, or if you have any other questions.

- Doctor Jubal, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Calculus
High School Trigonometry

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