Trig Equation: Solving for Theta with Tangent and Sine Functions

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SUMMARY

The discussion centers on solving the trigonometric equation Tan[60 degrees] = Sin[theta]/(1/3 + Cos[theta]). The user initially manipulates the equation but encounters confusion regarding the transformation of terms. A participant advises correcting the equation by separating sine and cosine, suggesting the use of a Pythagorean identity to express Sin[theta] in terms of Cos[theta]. Ultimately, the user successfully finds the solution of 1.34004 radians or 76.7786 degrees using Mathematica.

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lylos
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Homework Statement


Tan[60 degrees]=Sin[theta]/(1/3+Cos[theta])


Homework Equations


Trig identities?


The Attempt at a Solution


Tan[60 degrees]=Sin[theta]/(1/3+Cos[theta])
(1/3+Cos[theta])Tan[60 degrees]=Sin[theta]
1/3 Tan[60 degrees]=Sin[theta]-Tan[60 degrees]*Sin[theta]

Now I'm lost...
I can put it in mathematica, and get a solution of 1.34004 Radians or 76.7786 degrees. I just don't know how to solve it!
 
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lylos said:

The Attempt at a Solution


Tan[60 degrees]=Sin[theta]/(1/3+Cos[theta])
(1/3+Cos[theta])Tan[60 degrees]=Sin[theta]

OK so far.

1/3 Tan[60 degrees]=Sin[theta]-Tan[60 degrees]*Sin[theta]

The line is wrong. Your cosine morphed into a sine, so you'll need to fix that. I would actually back up to the previous line, leaving the cosine and sine on different sides. Look at \sin(\theta) on the right side. Use a Pythagorean identity to express it in terms of \cos(\theta).
 
Thank you, I was able to get to the solution!
 

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