Co-functions and Solving Trig Equations
Date: 11/18/2004 at 01:37:45 From: sara Subject: Trigonometry If sin(3x - 26)° = cos(5x - 60)°, find x. I tried: 3x - 26 = 5x - 60 2x = 60 - 26 2x = 34 x = 17 but it's not the right answer.
Date: 11/18/2004 at 08:56:32 From: Doctor Ian Subject: Re: Trigonometry Hi Sara, Note that you can't just set the two arguments equal to each other. That would only work if sin(A) = cos(A) Let's look at a right triangle, like this one: . . . 1 . B . . . u . . . A . . . . . . . . We know that sin(A) = opposite/hypotenuse, so sin(A) = u/1 = u cos(B) = adjacent/hypotenuse, so cos(B) = u/1 = u So sin(A) = cos(B) when A and B are complementary angles (two angles that add to make 90 degrees). This means that if sin(3x - 26) = cos(5x - 60) then (3x - 26) + (5x - 60) = 90 since the two angles must be complementary. Does this make sense? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
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