## Programs for Yr 12 Calculus:

 Title Function Instructions Remarks a.cos(t)+b.sin(t) Converts a*cos(t)+b*sin(t) to the form c*sin(t-d) or c*cos(t-d) You will be prompted for 'a' and 'b', and then given information as to workings, and the values of 'c' and 'd'. 'c' is given as an unsimplified surd as well as a number, in case exact values are asked for. 'd' is dependant on the current angle mode. cos(t)^n Expand cos(t)^n in terms of a*cos(b*t) You will be prompted for 'n'. The program will then display the expansion in stages. Trapezia Under F1(X) To approximate the area under F1(X) using trapezoids Enter the equation in question into F1(X). Run the program. You will be prompted for starting and ending X coordinates, and for the number of intervals to use. The program then calculates underestimated and overestimated areas, and the average (or trapezoidal) area. This aplet borrows the use of F1(X) from the Function aplet.  If there is more than one aplet on the calculator derived from 'Function', then the one highlighted in the LIB view is used. F1(X) Area F2(X) Calculates the unsigned area between the curves in F1(X) and F2(X) You will be prompted for the starting and ending values of X. The area will then be displayed. See the remark above about F1(X) which also applies here to both equations. This program can be VERY slow in some cases. It may be quicker to do the problem by hand. F1(X) Area y=0 Calculates the unsigned area between the curve in F1(X) and the x axis. As above. As above. Polar->Cart Convert a complex number in polar coordinates to cartesian form You will be prompted for the complex number. The program will then display the result. The result will be stored in Z1 The conversion depends on the current angle mode. Cart->Polar Convert a complex number in cartesian form to polar coordinates As above. As above. Divide Polynomials Divide a higher-order polynomial by a lower-order one. Used by factor and remainder theories, etc. You will be prompted for two polynomials in vector form:  a*x^(n) + b*x^(n-1) + c*x^(n-2) + ... + f * x^1 + g  is represented as [a, b, c, ..., f, g]  The result, and remainder after division, will be displayed. Polynomial terms can have complex coefficients.  'vector form' is the form used with PolyRoot, PolyCoef etc. SimpleSurd Simplify a surd You will be prompted for the square of the surd. eg. if the surd is sqrt(x), enter x.  The surd will be simplified, if possible, and expressed as  a * sqrt(b), where a^2 * b = x for example, if the surd is root(24) then enter 24. The output will be 2*sqrt(6). Small Increments Calculate an approximate small change given a small increment Enter an equation into F1(X), and run the program. You will be prompted for the small increment, and the resulting change will be displayed. This uses the approximation: delta(Y) ~= dY/dX * delta(X)