Solution for Trig EqualityDate: 7/27/96 at 17:4:16 From: Anonymous Subject: Solution for Trig Equality Hi Dr.Math! I am currently taking trig in high school and have stumbled upon an intresting math question that is kind of hard. It goes: Sin x = Cos x I have no idea what that means. One method I have tried is using sin(90-x) = cos and vice versa, but still it doesn't come out. Maybe using the inverse sin or cosine can work. Can you help me? I would really appreciate it. Thank you. Date: 7/27/96 at 19:16:15 From: Doctor Anthony Subject: Re: Solution for Trig Equality There are various relationships between the trig ratios. The two most commonly used are sin^2 x + cos^2 x = 1 sin x and tan x = ----- cos x In the question you asked about sin x = cos x sin x/cos x = 1 tan x = 1 This has two solutions in the range 0 to 360 degrees, namely 45 degrees and 180 + 45 = 225 degrees. In radians, the answers are pi/4 and 5*pi/4 You could now add multiples of 360 degrees (2*pi radians) to these solutions, to give all possible values of x that satisfy the equation. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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