Solve for x
Date: 10/26/2001 at 00:02:26 From: veronica Subject: Trig equations Please help me solve for x: Solve over (0,2pi) 1. tan^2 x = 2sec x - 1 2. sin x - sqrt3 cos x = 1 Thank you.
Date: 10/26/2001 at 11:40:13 From: Doctor Rob Subject: Re: Trig equations Thanks for writing to Ask Dr. Math, Veronica. 1. Use the identity tan^2(x) + 1 = sec^2(x), and convert this into a quadratic equation in sec(x). Solve it for sec(x). Then finish. 2. There is a general technique for equations of the form a*sin(x) + b*cos(x) = c. Divide by sqrt(a^2+b^2), and figure out the angle A such that cos(A) = a/sqrt(a^2+b^2), sin(A) = b/sqrt(a^2+b^2). Then the equation will take the form cos(A)*sin(x) + sin(A)*cos(x) = c/sqrt(a^2+b^2), sin(x+A) = c/sqrt(a^2+b^2). (Why?) That will allow you to figure out x + A, and thus x. In your case, a = 1 and b = -sqrt(3), so sqrt(a^2+b^2) = 2. Then cos(A) = 1/2, sin(A) = -sqrt(3)/2, so A = -60 degrees, or -Pi/3 radians. (Why?) You finish. - Doctor Rob, The Math Forum http://mathforum.org/dr.math/
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