Simple angle relationship question

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Homework Help Overview

The discussion revolves around the relationship between angles in trigonometric functions, specifically focusing on the equation tan(theta) = C*tan(gamma). Participants are exploring whether angles should be expressed in degrees or radians when solving for gamma.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the necessity of converting angles between degrees and radians and the implications of using a constant C in different units. There is also a discussion about the results obtained from different methods of calculation.

Discussion Status

The conversation is ongoing, with participants providing different perspectives on the relationship between the angles and the constant C. Some guidance has been offered regarding the consistency of units, but no consensus has been reached on the best approach to take.

Contextual Notes

There is a noted confusion regarding the use of degrees versus radians and the impact this has on the value of the constant C. Participants are also reflecting on the results they obtained through different methods of calculation.

jx44
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So I have a minor in mathematics yet I am confusing myself over the following - if I am given an angle, theta, in degrees and need to find a second angle, gamma, in degrees, and the relationship is tan(theta) = C*tan(gamma), where C is some constant, can I plug in theta in degrees and get gamma in degrees? Or do I need to convert theta to radians, find gamma in radians, then convert gamma to degrees again? If I do it with degrees I get 26.32, but if I do it the radians way i get 27.69.
 
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Careful, that constant is going to be different if you're using radians or degrees or arcseconds or what have you, if you just bounce around units and use the same constant, you'll be wrong
 
tan(15degrees)=(13/24)*tan(gamma)

gamma = arctan ((24/13)*tan(15 degrees))

gamma = 26.32
 
Ah, but you got the answer in radians originally, didn't you? Then you had to convert it to degrees

tan(15 degrees)=tan(.261...) they're the outright same number, that value for C will always without fail give you the answer in radians, regardless of what you use in the input
 

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