Problem 4 Many applications use the following "small angle" approximation for the sine to obtain a simpler model that is easy to understand and analyze. This approximate states that sin(x) ~ x, where a must be in radians. Investigate the accuracy of this approximation by creating three plots. For the first, plot sin(x versus x for 0 3S 1.For the second plot the approximation error sin(x) - versus x for 0 1. For the third plot the relative error [sin(x)-x|/sin(x) versus x for 01. How small must a be for the approximation to be accurate within 5 percent? Use the relative error for this calculation. (for example the relative error for v isp). Problem 5 The function y(t) = 1-e-bt, where t is time and b > 0, describes many processes such as height of liquid in a t ank as it is being filled and the temperature of an object being heated. Investigate the effect of the parameter b on y(t). To do this, plot y versus t for 0 3 t 10 seconds and b-0.01, 0.05, 0.1, 0.5, 1.0, 5.0, and 10.0 on the same plot. How long will it take for y(t) to reach 98 percent of its steady-state when b=0.5