



 
Hi David. The question involves the distance between the origin and a point on a graph, so I first think about how to calculate distances on a graph. You can demonstrate to yourself that the distance from the origin to any point (x,y) on a cartesian graph is simply the square root of the sum of the squares x^{2} and y^{2}. This is because the distance is the hypotenuse of a right triangle whose other sides are x and y, so Pythagoras gives us this expression. So I start by calling the distance w and I write the equation: Next, I need to know something about x and y. We are given the equation y = sin x, so I can substitute sin x in for y in my equation. That's good: one equation with two variables. Now I look at the question again. It is asking for the "rate of change of the distance". Well, I know that that is the derivative of the distance with respect to time, which in variables means dw/dt. To find that, I have to take the derivative of both sides of my equation: Clearly, I next would have to take the derivative of that expression and I'm going to need the chain rule more than once. I hope you have been studying the chain rule, David, because I'll leave the derivation to you. You will get, on the left side of the equal sign, an expression with x in it as well as dx/dt in it. The last step is to look at a particular value of dx/dt. You simply substitute in what you are given (that dx/dt equals 2 cm/sec) and simplify. You will still have the value x in there, of course, because you weren't given a value for it. So don't expect a single number as your answer. To review, when solving this kind of question, I
Hope this helps,  


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