Trigonometric Expressions

sin(xy)=cos(xy)

sin(x)^y = x siny

\cos(x)+\sin(x*y)=\cos(y*x)+\sin(y)

\sin y=\cos x

Algebraic Equations

x!!=y!!

\log_{x}(y)=1/(\log_{y}(x))

#define _USE_MATH_DEFINES
#include <math.h>
#include <iostream>
#include <iomanip>

/**
 * Estimate PI using Leibiniz series
 * 1 - (1/3) + (1/5) - (1/7) + (1/9) .... = (pi / 4)
 */

void calc(int terms) {
    long double pi = M_PI;

    long double sum = 0;
    long long int denom = 1;

    for(int i = 0; i < terms; i++) {
        sum += pow(-1, i) * ( 1 / double(denom) );
        denom += 2;
        long double estimate = sum * 4;
        long double diff = abs(pi - estimate);
        std::cout ...

Aim - Create a C++ program to draw an arrow:

• between 2 given coordinates
• arms of length as a given ratio to its body length
• arms at specified incline to the body

Given:

• Start point of arrow as (x1, y1) and end point (x2, y2). Eg: (2, 3) and (10, 100)
• Ratio provided = x : y. Eg 1:10
• Incline of arrow arms (in degrees) = θ. Eg: θ=67

Attempt 1

Attempt 1 relies on individually calculating the slope of all 3 lines and finding points of the arrow by combining equations of distance formula, tangent slope for...

Basic Performance Tests

$ ./a.exe 500000
std::list: 5359224 ms
list: 5368370 ms
$ ./a.exe 200000
std::list: 536497 ms
list: 487405 ms