100sin(alpha) = 500cos(alpha) - how do you solve such a thing?

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To solve the equation 100sin(alpha) = 500cos(alpha), one effective approach is to divide both sides by cos(alpha), which simplifies the equation to a tangent function: tan(alpha) = 100/500. Alternatively, squaring both sides can also help, utilizing the Pythagorean identity relating sine and cosine. Understanding the relationship between sine and cosine is crucial for solving trigonometric equations. This method allows for easier manipulation and finding the angle alpha.
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100sin(alpha) = 500cos(alpha) ---- how do you solve such a thing?

100sin(alpha) = 500cos(alpha)

I see there's only one unknown, but I'm a little befuddled how to approach trigo equations like that when the angle is unkown (I know about the arc-cos/sin/tan function) but there are 2 functions in the equation! Cosine AND Sine! Arg... perhaps you guys can help me with a short guide/link/whatever...

I'll appreciate the help :)

-Dory
 
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Why don't you square both sides. Do you know of any relation relating squares of sines and cosines?
 


Or even more simply, divide through by \cos(\alpha)
 


Thanks! Right, I forgot that sine/cosine is tan! :) That simplifies things!
 


Mentallic said:
Or even more simply, divide through by \cos(\alpha)

Oh! :P
 

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