Level 1)Develop a procedure that will calculate the radius and the angle for giv
ID: 1947592 • Letter: L
Question
Level 1)Develop a procedure that will calculate the radius and the angle for given specific numbers for an arc and a cord. For example, if arc = 1.5 and cord = 1, calculate r and [Theta]. You should write that procedure and demonstrate that it works for these specific numbers.Level 2)Improve the procedure from Level 1 in such a way that it would work for any "legal" arc and cord. Ideally, this procedure should not require any additional user input. Write your procedure as a function with two inputs: arc and cord, and two outputs: the corresponding radius and angle. In other words define the function AC2RA. Make the variable a list {arc,cord}. The output of this function should be the list of the corresponding radius and angle: {radius,angle}. Notice that the above function is in fact the inverse of the function that I describe in the following cell. Working on Level 1 and Level 2 you probably know how to calculate the arc and the cord when radius and the angle are given. Make this into a function. In other words define the function RA2AC. Make the variable a list {radius,angle}. The output of this function should be the list of the corresponding arc and cord: {arc,cord}.The definition of the function AC2RA is more complicated. Make sure that it is correct by calculating AC2RA[RA2AC[{radius,angle}]] Do this calculation for a large number of values for radius and angle. In fact you can cover all possible angles (0,2 [Pi]) and, for example, radii between 0.2 and 5.
Level 3)Assume that this question was asked by a local carpenter who encounters such calculation often and needs an efficient tool to do it on a construction site. Assume that the carpenter has only a scientific calculator. Help this carpenter calculate the radius and the angle for any "legal" arc and cord that he will encounter at his construction site.
Explanation / Answer
Level 1)Develop a procedure that will calculate the radius and the angle for given specific numbers for an arc and a cord. For example, if arc = 1.5 and cord = 1, calculate r and [Theta]. You should write that procedure and demonstrate that it works for these specific numbers. LET ARC LENGTH = A LET CHORD LENGTH = C LET THE ANGLE OF THE ARC BE T IN RADIANS = T*180/ IN DEGREES LET THE RADIUS = R WE HAVE THE FORMULAS A=R*T..............T=A/R.............................1 C= 2R*SIN[0.5T]..............................2 PROCEDURE.... 1.TABULATE AS SHOWN BELOW.. N...IS NUMBER OF TRIAL T ASSUMED...IS T USED FOR CALCULTION IN RADIANS ..... R...IS R CALCULATED USING THE ABOVE T T-CALCULATED IS T FOUND USING R CALCULATED ABOVE AND GIVEN VALUE OF A . T[IN DEGREES ] ..JUST SHOWN FOR USE IF NEEDED ..NOT REALLY NECESSARY ... 2. START WITH AN ASSUMED VALUE OF T ..SAY 0.1 GIVEN IN THE EXAMPLE. 3.FIND R FROM EQN.2 USING GIVEN VALUE OF C AND ASSUMED T 4.FIND T-CALC. FROM EQN.1 USING GIVEN VALUE OF A AND R OBTAINED UNDER 3 . 5. USE THIS VALUE OF T FOR TRIAL NUMBER 2 AND REPEAT TILL DESIRED ACCURACY IS OBTAINED. 6. THAT IS T ASSUMED AND T CALCULATED SHALL EQUAL TO DESIRED LEVEL OF ACCURACY .. R= 10 T= 0.174510 DEGREES
C= 1.74311 A= 1.7453 N T ASSUMED R=C/[2*SIN(0.5T)] T-CALC. T IN DEG. 1 0.1 17.43836508 0.100083924 5.729577951 2 0.100083924 17.42375462 0.100167848 5.734386426 3 0.100167848 17.40916859 0.100251772 5.739194919 4 0.100251772 17.39460697 0.100335696 5.744003422 5 0.100335696 17.38006973 0.10041962 5.748811924 6 0.10041962 17.36555682 0.100503544 5.753620415 7 0.100503544 17.35106822 0.100587467 5.758428885 8 0.100587467 17.33660391 0.100671389 5.763237323 9 0.100671389 17.32216385 0.100755311 5.76804572 10 0.100755311 17.307748 0.100839231 5.772854065 11 0.100839231 17.29335635 0.10092315 5.777662349 12 0.10092315 17.27898885 0.101007068 5.782470561 13 0.101007068 17.26464549 0.101090984 5.78727869 Level 2)Improve the procedure from Level 1 in such a way that it would work for any "legal" arc and cord. Ideally, this procedure should not require any additional user input. Write your procedure as a function with two inputs: arc and cord, and two outputs: the corresponding radius and angle. In other words define the function AC2RA. Make the variable a list {arc,cord}. The output of this function should be the list of the corresponding radius and angle: {radius,angle}. Notice that the above function is in fact the inverse of the function that I describe in the following cell. Working on Level 1 and Level 2 you probably know how to calculate the arc and the cord when radius and the angle are given. Make this into a function. In other words define the function RA2AC. Make the variable a list {radius,angle}. The output of this function should be the list of the corresponding arc and cord: {arc,cord}.The definition of the function AC2RA is more complicated. Make sure that it is correct by calculating AC2RA[RA2AC[{radius,angle}]] Do this calculation for a large number of values for radius and angle. In fact you can cover all possible angles (0,2 [Pi]) and, for example, radii between 0.2 and 5. SAME A ABOVE DEPENDING ON THE LEVEL WE FIX THE ACCURACY LEVEL FOR EX..IN LEVEL 1 WE MAY SPECIFY 1% ACCURACY , WHILE IN LEVEL 2 WE MAY APPLY 0.01% ACCURACY Level 3)Assume that this question was asked by a local carpenter who encounters such calculation often and needs an efficient tool to do it on a construction site. Assume that the carpenter has only a scientific calculator. Help this carpenter calculate the radius and the angle for any "legal" arc and cord that he will encounter at his construction site. SAME PROCEDURE IS ADOPTABLE ON CALCULATOR .... R= 10 T= 0.1745
10 DEGREES
C= 1.74311 A= 1.7453 N T ASSUMED R=C/[2*SIN(0.5T)] T-CALC. T IN DEG. 1 0.1 17.43836508 0.100083924 5.729577951 2 0.100083924 17.42375462 0.100167848 5.734386426 3 0.100167848 17.40916859 0.100251772 5.739194919 4 0.100251772 17.39460697 0.100335696 5.744003422 5 0.100335696 17.38006973 0.10041962 5.748811924 6 0.10041962 17.36555682 0.100503544 5.753620415 7 0.100503544 17.35106822 0.100587467 5.758428885 8 0.100587467 17.33660391 0.100671389 5.763237323 9 0.100671389 17.32216385 0.100755311 5.76804572 10 0.100755311 17.307748 0.100839231 5.772854065 11 0.100839231 17.29335635 0.10092315 5.777662349 12 0.10092315 17.27898885 0.101007068 5.782470561 13 0.101007068 17.26464549 0.101090984 5.78727869
Related Questions
Hire Me For All Your Tutoring Needs
Integrity-first tutoring: clear explanations, guidance, and feedback.
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.