Obliterating Iterating (Fazed by Phase)Date: 10/10/2003 at 11:46:16 From: Howard Subject: Trig Equation What is the solution for angle [theta] where: a*sin[theta] + b*cos[theta] = c with a, b and c being constants? I can find a solution by iteration, but intuitively it seems that there must be a better way. This is a generalisation of a real-world problem to find the necessary final inclination of a line attached to a circular arc reaching a defined lateral and vertical displacement. Date: 10/10/2003 at 12:17:10 From: Doctor George Subject: Re: Trig Equation Hi Howard, Thanks for writing to Doctor Math. Although your question wasn't asked in the context of phase calculations, that is a common place for this question to come up. First divide though by sqrt(a^2 + b^2) to get a b --------------- sin[theta] + --------------- cos[theta] sqrt(a^2 + b^2) sqrt(a^2 + b^2) c = --------------- sqrt(a^2 + b^2) Now define alpha such that a b cos[alpha] = --------------- and sin[alpha] = --------------- sqrt(a^2 + b^2) sqrt(a^2 + b^2) Now we have c cos[alpha]sin[theta] + sin[alpha]cos[theta] = --------------- sqrt(a^2 + b^2) Can you finish it from there? Write again if you need more help. - Doctor George, The Math Forum http://mathforum.org/dr.math/ Date: 10/13/2003 at 13:32:04 From: Howard Moles Subject: Thank you (Trig Equation) Thanks Dr George! I now recognise the solution, but it has been almost 40 years since I first saw it. Howard |
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