As the first part of a related rate problem, I am asked to find equations for the position of the tip of a crankshaft with length 2in and center of rotation at the origin. The crankshaft makes 2 complete rotations per second. The equation needs to be represented in t seconds.
I know that the equation of a circle is x^2+y^2=r^2, but I cannot use this because I have no way to relate time to those values. If I substitute cosine for x and sine for y, I just get a straight line, because that will always equal a constant.
I know that parametric equations would work,but I think I am supposed to find "functions"; although, the book does state "find equations" so, I suppose parametric equations are not forbidden.
I cannot think of any other way to represent the periodic nature of the position of the tip of the crankshaft.
Is there a way to represent the position with a normal function, or must parametric functions be used?
I would ask a professor or teacher, but I am reviewing on my own before I start college, so I don't have access to such resources right now.
Finally, this is part of a Calculus question, but it is initimately related to Trigonometry as well. I am not sure where I should post this. If it should be moved, please let me know. Thank you.