The discussion centers on the feasibility of substituting trigonometric functions with their Cartesian equivalents, specifically using the expression 5Cos(x)/(Sin(x)-1). Participants confirm that it is possible to express sine and cosine in terms of x and y, with the substitution sin(x) = y being a common approach. The conversation emphasizes the importance of reverting to trigonometric identities after manipulation. This method allows for easier problem-solving in trigonometry when expressed in Cartesian coordinates.
PREREQUISITESStudents studying trigonometry, educators teaching trigonometric concepts, and anyone looking to enhance their problem-solving skills in mathematics through the use of Cartesian coordinates.
Yeah, you can substitute,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 solveTyrion101 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?