Chapter. Program Library

Transcription

1 hapter Program ibrary Prime actor nalysis reatest ommon easure t-est Value ircle and angents otating a igure efore using the Program ibrary e sure to check how many bytes of unused memory is remaining before attempting to perform any programming. his Program ibrary is divided into two sections a numeric calculation section and a graphics section. Programs in the numeric calculation section produce results only while graphics programs use the entire display area for graphing. lso note that calculations within graphics programs do not use the multiplication sign wherever it can be dropped i.e. in front of open parenthesis.

2 P H Program for Prime actor nalysis o. escription Produces prime factors of arbitrary positive integers or < m < Prime numbers are produced from the lowest value first. is displayed at the end of the program. verview m is divided by and by all successive odd numbers d... to check for divisibility. here d is a prime factor mi mi/d is assumed and division is repeated until mi < d. xample [] [] [] Preparation and operation tore the program written on the next page. xecute the program as shown below. tep Key operation isplay tep Key operation isplay

3 P rac rac H J K P U V mi d mi o. ine Program ile name emory ontents

4 P H Program for reatest ommon easure o. escription uclidean general division is used to determine the greatest common measure for two interers a and b. or a b < positive values are taken as < verview n max a b n min a b nk nk nk nk nk k... f nk then the greatest common measure c will be nk. xample [] [] [] hen a a a b b b c c c Preparation and operation tore the program written on the next page. xecute the program as shown below. tep Key operation isplay tep Key operation isplay

5 bs < bs lnt H J K P U V a n b n n k o. ine Program ile name emory ontents

6 P H Program for t-est Value o. escription he mean sample mean and sample standard deviation can be used to obtain a t-test value. t x m x n n x xσn n m mean of x data sample standard deviation of x data number of data items hypothetical population standard deviation normally represented by µ but m is used here because of variable name limitations xample o determine whether the population standard deviation for sample data is. Perform a t-test with a level of significance of %. Preparation and operation tore the program written on the next page. xecute the program as shown below. tep Key operation isplay tep Key operation isplay he above operation produces a t-test value of t.. ccording to the t-distribution table in the next page a level of significance of % and a degree of freedom of n produce a two-sided t-test value of approximately.. ince the calculated t-test value is lower than the table value the hypothesis that population mean m equals is accepted.

7 o. ine Program ile name { l-var ist x } ist xσn n emory ontents H J K m P U t V t-distribution table he values in the top row of the table show the probability two-sided probability that the absolute value of t is greater than the table values for a given degree of freedom. a a P Probability egree of reedom

8 P H Program for ircle and angents o. escription x'y' r ormula for circle x y r ormula for tangent line passing through point x' y' y y' m x x' * m represents the slope of the tangent line ith this program slope m and intercept b y' mx' are obtained for lines drawn from point x' y' and are tangent to a circle with a radius of r. he trace function is used to read out the coordinates at the points of tangency and factor zoom is used to enlarge the graph. xample o determine m and b for the following values r x' y' otes he point plotted for cannot be moved. ven if it is moved on the graph the calculation is performed using the original value. n error a occurs when r x'. e sure to always perform a trace operation whenever you select trace and the message is on the display. Preparation and operation tore the program written on the next page. xecute the program as shown below. emory ontents H J K P U V

9 Prog Prog raph raph x actor x P x x P x x x x x P x x actor x x o. ine Program ile name

10 View indow Prog raph raph Prog raph raph. raph x x. x x Prog.. o. ine Program ile name ile name

11 Program for ircle and angents tep Key peration isplay o.

12 Program for ircle and angents tep Key peration isplay o.

13 Program for ircle and angents tep Key peration isplay o.

14 Program for ircle and angents tep Key peration isplay o.

15 P H Program for otating a igure o. escription ormula for coordinate transformation x y x' y' x' x cos θ y sin θ y' x sin θ y cos θ x y x y x y xample raphing of rotation of any geometric figure by θ degrees. o rotate by the triangle defined by points.. and. otes Use the cursor keys to move the pointer around the display. o interrupt program execution press while the graphic screen is on the display. he triangle cannot be drawn if the result of the coordinate transformation operation exceeds View indow parameters. Preparation and operation tore the program written on the next page. xecute the program as shown below. emory ontents x y x y x y x' H J K y' x' y' x' y' P U V

16 o. ine Program ile name ine ls cos sin cos sin cos sin K. H J H eg sin cos sin cos ine sin cos ine ine. ine eg H J K. ine View indow.

17 Program for otating a igure tep Key peration isplay o.

18 Program for otating a igure tep Key peration isplay o. ocate the pointer at ontinue repeating from step.