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/
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