Untitled

Basic Math Operations Using C++

Introduction to Basic Mathematical Operations in C++

• C++ is capable of performing basic mathematical operations.
• Example program demonstrating these mathematical operations:

  #include<iostream>
  using namespace std;
  int main() {
      int number1;
      int number2;
      int result;
      cout<<"Please enter number1 & number2";
      cin>>number1>>number2;
      result = number1 + number2; 
      result = number1 - number2;  
      result = number1 * number2;  
      result = number1 / number2;  
      result = number1 % number2;  
      cout<<result;
      return 0;
  }

Explanation of Program Components

• Operands: The variables number1 and number2 are operands in the expressions.
• Operators: Various operators are used, including addition (+), subtraction (-), multiplication (*), division (/), and modulus (%).
• Modulus Operator: The modulus operator is only applicable for integer data types.
• Division Behavior: The division of integers yields an integer result, truncating any decimals. This necessitates understanding order of precedence among the arithmetic operators.

Example of Operator Precedence and Outcomes

• Two illustrative cases of operator precedence in C++:

Case I

y = 5 / 2 * 5 + 3 * 5 + 7;
cout<<y;

• Expected Output: y = 32

Case II

y = 5 * 5 / 2 + 3 * 5 + 7;
cout<<y;

• Expected Output: y = 34

Precedence of Arithmetic Operators

• Order of Operations:
  • ( ) Parentheses: Evaluated first. Inner expressions take precedence when nested.
  • *, /, %: Multiplication, division, and modulus are evaluated second from left to right.
  • +, -: Addition and subtraction are evaluated last, also from left to right.

Example Code Demonstrating Averaging

• Initial implementation of average calculation (Incorrect due to precedence):

  #include<iostream>
  using namespace std;
  int main() {
      int number1 = 74, number2 = 82, number3 = 88;
      double average;
      average = number1 + number2 + number3 / 3;  // Incorrect
      cout<<average;
      return 0;
  }

• Correct approach which uses parentheses to ensure correct order:

  #include<iostream>
  using namespace std;
  int main() {
      int number1 = 74, number2 = 82, number3 = 88;
      double average;
      average = (number1 + number2 + number3) / 3;  // Correct
      cout<<average;
      return 0;
  }

Using Constant Variables

• Code example utilizing a constant for grades:

  #include<iostream>
  using namespace std;
  int main() {
      int number1 = 74, number2 = 82, number3 = 88;
      double average;
      const int numGrades = 3;
      average = (number1 + number2 + number3) / numGrades;
      cout<<average;
      return 0;
  }

• Any attempt to modify a constant variable results in a compilation error: "Error: assignment of read-only variable."
• Constants are beneficial for repeated usage, such as the mathematical constant pi in calculations.

Advanced Mathematical Functions in C++

• Various mathematical functions are available through the <cmath> library. To include this library, use:

  #include<cmath>

Category of Functions

• Trigonometric Functions:

  • cos(x): Returns cosine of angle x in radians.
  • sin(x): Returns sine of angle x in radians.
  • tan(x): Returns tangent of angle x in radians.
  • acos(x): Computes the principal value of arc cosine; domain error for inputs not in [-1, 1].
  • asin(x): Computes the principal value of arc sine; similar domain restrictions.
  • atan(x): Returns arc tangent in range [−π/2, +π/2].

• Exponential and Logarithmic Functions:

  • exp(x): Returns e raised to power x.
  • log(x): Natural logarithm of x; domain error for negative values.
  • log10(x): Common logarithm (base 10) of x; domain error for negative values.

• Power Functions:

  • pow(base, exponent): Returns base raised to the power of exponent e.g., pow(7.0, 3.0) gives 7^3.
  • sqrt(x): Returns square root; domain error for negative values.
  • cbrt(x): Returns cubic root of x.

• Rounding and Remainder Functions:

  • ceil(x): Rounds x upward to nearest integral value.
  • floor(x): Rounds x downward to nearest integral value.
  • fmod(numerator, denominator): Returns floating-point remainder of division.
  • trunc(x): Rounds x toward zero.
  • round(x): Rounds to nearest integral value, with halfway cases away from zero.

• Absolute Value Functions:

  • fabs(x): Returns absolute value of x: |x|.
  • abs(x): Returns absolute value as well.

Example of Using Trigonometric Functions

• Example code to calculate trigonometric ratios:

  #include<iostream>
  #include<cmath>
  using namespace std;
  int main() {
      const double pi = 3.141592;
      double angle = pi/6;
      cout<<"******** Calculating Trigonometric Ratios ********"<<endl;
      cout<<"All calculations on Angle "+to_string(angle)+" Radians"<<endl;
      cout<<"cos("<<angle<<") = "<<cos(angle)<<endl;
      cout<<"sin("<<angle<<") = "<<sin(angle)<<endl;
      cout<<"tan("<<angle<<") = "<<tan(angle)<<endl;
      cout<<"******** Calculations Terminated ********"<<endl;
      return 0;
  }

• Task: Write a program to take angle input from the user in degrees and find its cosine, sine, and tangent.

Using Exponential and Logarithmic Functions

• Example program using logarithmic functions:

  #include<iostream>
  #include<cmath>
  using namespace std;
  int main() {
      double num = 10.3;
      cout<<"exp("<<num<<") = "<<exp(num)<<endl;
      cout<<"log("<<num<<") = "<<log(num)<<endl;
      cout<<"log10("<<num<<") = "<<log10(num)<<endl;
      return 0;
  }

Using Power Functions Example

• Example program for power functions:

  #include<iostream>
  #include<cmath>
  using namespace std;
  int main() {
      double num1 = 10.3, num2 = 2.0;
      cout<<"pow("<<num1<<","<<num2<<") = "<<pow(num1,num2)<<endl;
      cout<<"sqrt("<<num1<<") = "<<sqrt(num1)<<endl;
      cout<<"cbrt("<<num1<<") = "<<cbrt(num1)<<endl;
      return 0;
  }

Using Rounding and Remainder Functions Example

• Example demonstrating rounding functions:

  #include<iostream>
  #include<cmath>
  using namespace std;
  int main() {
      double num1 = 2.3, num2 = 3.8, num3 = 5.5, num4 = -2.3, num5 = -3.8, num6 = -5.5;
      cout<<"value\tround\tfloor\tceil\ttrunc\n";
      cout<<"-----\t-----\t-----\t----\t-----\n";
      cout<<num1<<"\t"<<round(num1)<<"\t"<<floor(num1)<<"\t"<<ceil(num1)<<"\t"<<trunc(num1) <<"\n";
      cout<<num2<<"\t"<<round(num2)<<"\t"<<floor(num2)<<"\t"<<ceil(num2)<<"\t"<<trunc(num2) <<"\n";
      cout<<num3<<"\t"<<round(num3)<<"\t"<<floor(num3)<<"\t"<<ceil(num3)<<"\t"<<trunc(num3) <<"\n";
      cout<<num4<<"\t"<<round(num4)<<"\t"<<floor(num4)<<"\t"<<ceil(num4)<<"\t"<<trunc(num4) <<"\n";
      cout<<num5<<"\t"<<round(num5)<<"\t"<<floor(num5)<<"\t"<<ceil(num5)<<"\t"<<trunc(num5) <<"\n";
      cout<<num6<<"\t"<<round(num6)<<"\t"<<floor(num6)<<"\t"<<ceil(num6)<<"\t"<<trunc(num6) <<"\n";
      return 0;
  }

Understanding Floating Points and Type Casting

• Example of type casting in C++:

  #include<iostream>
  #include<cmath>
  using namespace std;
  int main() {
      float num1 = -9.5;
      int num2 = 101;
      cout<<(int)num1;
      cout<<endl<<(float)num2/10;
      return 0;
  }

Formatting Output with

• Sample code to demonstrate output control using <iomanip>:

  #include<iostream>
  #include<cmath>
  #include<iomanip>
  using namespace std;
  int main() {
      double planck = 6.62607004e-34;
      double gravitation = 6.67408e-11;
      double charge = 1.60217662e-19;
      cout<<"********Output Without Precision********"<<endl;
      cout<<"Planck's Constant = "+to_string(planck)<<endl;
      cout<<"Gravitational Constant = "+to_string(gravitation)<<endl;
      cout<<"Charge on electron = "+to_string(charge)<<endl;
      cout<<"********Output with Precision of 10********"<<endl;
      cout<<setprecision(10);
      cout<<"Planck's Constant = "+to_string(planck)<<endl;
      cout<<"Gravitational Constant = "+to_string(gravitation)<<endl;
      cout<<"Charge on electron = "+to_string(charge)<<endl;
      return 0;
  }

Exercises and Additional Tasks

• Write a note on the importance of operator precedence and why calculators handle this differently.
• Explore using <cmath> functions applied to integer types and address possible issues.
• Experiment with formatting functions scientific and fixed in C++ for different outputs.
• Implement expressions such as:
  • $| x + y |$
  • $|x| + |y|$
  • $x^3 y + y$
  • $ext{sqrt}(x^6 + y^5)$
  • $(x + ext{sqrt}(y))^7$
• Test erroneous inputs on functions such as:
  • $ext{sqrt}$
  • $ext{acos}$
  • $ext{atan}$
  • $ext{asin}$