In this task, you are required to write a code which takes as an input an angle [0°, 90°] in radians and returns the approximate value of the cosine of this angle. The code will also take as an input the number of terms to be used to approximate the result. We will use the Maclaurin series of cos(x) to approximate the result. The series is given by: cos(x) -1n2n = ΣX n=0 (2n!)
In this task, you are required to write a code which takes as an input an angle [0°, 90°] in radians and returns the approximate value of the cosine of this angle. The code will also take as an input the number of terms to be used to approximate the result. We will use the Maclaurin series of cos(x) to approximate the result. The series is given by: cos(x) -1n2n = ΣX n=0 (2n!)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
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Author:James Kurose, Keith Ross
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![In this task, you are required to write a code which takes as an input an angle
[0°, 90°] in radians and returns the approximate value of the cosine of this
angle. The code will also take as an input the number of terms to be used to
approximate the result.
We will use the Maclaurin series of cos(x) to approximate the result. The
series is given by:
cos(x)
=
Σn=0
-1"x2n
(2n!)
but for practical reasons, we will not use infinite terms but k terms where k is
input by the user:
cos(x)
=
Σ
-1x2n
2n=0 (2n!)
So, for example, to calculate the cosine for 60° (1.04667 radians) using five
terms, the approximation will be:
1.04667²
1
1.04667¹
4!
1.046676 1.046678
+
0.50046
2!
6!
8!
• The program should at most handle 15 terms (to avoid overflows due
to factorial), otherwise the program outputs Invalid
• There should be at least three terms used in the approximation,
otherwise the program outputs Invalid
• If the number of terms is negative, the programs corrects it
automatically to positive.
• If the angle is out of range, the program outputs Invalid
1/0
Program Input:
A single line that takes in any angle (in radians)
• A single line that takes in the number of terms to use in the
approximation
Program Output:
• A single line that outputs the approximate value of the cosine](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F14aa93be-3d7a-4f58-94cc-382dc4d854bb%2F62944f85-df8f-4ba6-9627-e8817a5f1945%2F1dsi3b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In this task, you are required to write a code which takes as an input an angle
[0°, 90°] in radians and returns the approximate value of the cosine of this
angle. The code will also take as an input the number of terms to be used to
approximate the result.
We will use the Maclaurin series of cos(x) to approximate the result. The
series is given by:
cos(x)
=
Σn=0
-1"x2n
(2n!)
but for practical reasons, we will not use infinite terms but k terms where k is
input by the user:
cos(x)
=
Σ
-1x2n
2n=0 (2n!)
So, for example, to calculate the cosine for 60° (1.04667 radians) using five
terms, the approximation will be:
1.04667²
1
1.04667¹
4!
1.046676 1.046678
+
0.50046
2!
6!
8!
• The program should at most handle 15 terms (to avoid overflows due
to factorial), otherwise the program outputs Invalid
• There should be at least three terms used in the approximation,
otherwise the program outputs Invalid
• If the number of terms is negative, the programs corrects it
automatically to positive.
• If the angle is out of range, the program outputs Invalid
1/0
Program Input:
A single line that takes in any angle (in radians)
• A single line that takes in the number of terms to use in the
approximation
Program Output:
• A single line that outputs the approximate value of the cosine
Transcribed Image Text:Sample Testcase 0:
Input:
1.04667
5
Output:
0.5004572
Sample Testcase 1:
Input:
1.04667
20
Output:
Invalid
1 #include <iostream>
2 #include <<math>
3 #include <iomanip>
4 using namespace std;
5
6 int main()
7
{
8
double x;
9
int k;
10
double sum = 0;
11
cin>>x;
12
cin>>k;
13
14
// Write your code here
15
16
17
18
// End Your code
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