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Solution for Trig Equality

Date: 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
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Associated Topics:
High School Trigonometry

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