Graph of the derivative of the sine curve
a. Use the graph of y = sin x (see figure) to sketch the graph of the derivative of the sine function.
b. Based upon your graph in part (a), what function equals \(\frac{d}{dx}(\sin x)\)?
SOLUTION STEP 1 (a). We need to sketch the derivative of the given sine graph We know that f(x)is the slope of the tangent at the point (x,f(x)) on the graph of f. From this graph we can find that at points x = and at x = 3 the slope is 0. Thus the graph 2 2 of y’ intercepts the x axis at these points. Then we can find that the slope is positive(ie, increasing slope) from x = to x = and f2om x = the slope decreases(ie,negative) upto x = 3and then it again increases upto x = 2 2 2 .Thus the graph of the derivative will be This is the graph of a cosine function. STEP 2 (b).Thus we can see that the derivative of the sine function is cosine function Therefore dxsin x = cos x
