Trig - Addition Formula Question

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Homework Help Overview

The discussion revolves around solving the equation cos(x-60)=sinx, which involves trigonometric identities and equations. The subject area is trigonometry, specifically focusing on addition formulas and their application in solving equations.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants attempt to manipulate the equation using trigonometric identities, specifically the cosine addition formula. There are various approaches suggested, including re-expressing sin(x) in terms of cosine. Some participants question the effectiveness of the initial method and suggest alternative strategies.

Discussion Status

The discussion is ongoing, with participants providing different methods and questioning the assumptions behind their approaches. Some guidance has been offered regarding alternative expressions for sin(x) and the implications of manipulating the equation further.

Contextual Notes

Participants are working within the constraint of finding solutions for x in the range of 0 to 360 degrees. There is a focus on ensuring that the methods discussed adhere to this range while exploring various interpretations of the problem.

studentxlol
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Homework Statement



Solve the equation cos(x-60)=sinx

Homework Equations



cosAcosB+sinAsinB

The Attempt at a Solution



cos(x-60)=sinx
cosxcos60+sinxsin60=sinx
1/2cosx+(√3)/2sinx=sinx

How do I then solve to find x for0<x<360
 
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studentxlol said:

Homework Statement



Solve the equation cos(x-60)=sinx

Homework Equations



cosAcosB+sinAsinB

The Attempt at a Solution



cos(x-60)=sinx
cosxcos60+sinxsin60=sinx
1/2cosx+(√3)/2sinx=sinx

How do I then solve to find x for0<x<360

Subtract sin(x) from both sides.

Divide by cos(x).
 
studentxlol said:

Homework Statement



Solve the equation cos(x-60)=sinx

Homework Equations



cosAcosB+sinAsinB

The Attempt at a Solution



cos(x-60)=sinx
cosxcos60+sinxsin60=sinx
1/2cosx+(√3)/2sinx=sinx

How do I then solve to find x for0<x<360

Suggestion: don't even do it this way.

You know that sin x = cos (90-x)

So re-express RHS like that:

cos (x-60) = cos (90-x)

x-60 = 90-x + 360n (where n is an integer)

2x = 150 + 360n

x = 75 + 180n

So x = 75 or 255 for n = 0 and 1 respectively. Those are the only two solutions in the required range.
 
studentxlol said:

Homework Statement



Solve the equation cos(x-60)=sinx

Homework Equations



cosAcosB+sinAsinB

The Attempt at a Solution



cos(x-60)=sinx
cosxcos60+sinxsin60=sinx
1/2cosx+(√3)/2sinx=sinx

How do I then solve to find x for0<x<360

SammyS said:
Subtract sin(x) from both sides.

Divide by cos(x).

Did you try what I suggested ?

What did you get ?

(1/2)cos(x)+((√3)/2-1)sin(x)=0

Now, divide by cos(x) .

[itex]\displaystyle \frac{\sin(x)}{\cos(x)}=\tan(x)[/itex] ---- Right?
 

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