Trig functions in terms of x,y, and r?

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The discussion revolves around the feasibility of expressing trigonometric functions in terms of x and y, specifically using substitutions like sin(x) = y. Participants confirm that substitution is possible, allowing for expressions such as 5Cos(x)/(Sin(x)-1) to be rewritten. However, clarity is sought regarding the definitions of sine and cosine being used, particularly in relation to triangles or unit circles. The conversation emphasizes the importance of correctly replacing trigonometric identities after substitution to solve the problems effectively. Overall, substituting trigonometric functions can aid in problem-solving if done carefully.
Tyrion101
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I work a good deal better when the equation is in x and y form, is it possible to set up a trig expression like 5Cos(x)/(Sin(x)-1)and substitute the proper x or y equivalent so long as I remember to replace the trig identities later when the problem is finished? Or can you just not solve these problems like this?
 
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Tyrion101 said:
I work a good deal better when the equation is in x and y form, is it possible to set up a trig expression like 5Cos(x)/(Sin(x)-1)and substitute the proper x or y equivalent so long as I remember to replace the trig identities later when the problem is finished? Or can you just not solve these problems like this?
Yeah, you can substitute,
Take sin x = y,
Then what should be cosx in terms of y ?
 
Tyrion101 said:
I work a good deal better when the equation is in x and y form, is it possible to set up a trig expression like 5Cos(x)/(Sin(x)-1)and substitute the proper x or y equivalent so long as I remember to replace the trig identities later when the problem is finished? Or can you just not solve these problems like this?
By ``proper x or y equivalent'' do you mean the types of definitions for sine and cosine we commonly attach to their definitions from triangles or unit circles? I' not sure what you're meaning is, or of the type of problem you are intending to solve
 

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