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Computer Science 1620. Math Library. Remember this program? suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) one year, b) two years c) three years. - PowerPoint PPT Presentation
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Computer Science 1620
Math Library
Remember this program?suppose that I invest $25000 into a mutual
fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) one year, b) two years c) three years
Suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) one year, b) two years c) three years
#include <iostream> using namespace std;
int main() {
cout << "Year 1: $" << 25000 * 1.08 << endl; cout << "Year 2: $" << 25000 * 1.08 * 1.08 << endl; cout << "Year 3: $" << 25000 * 1.08 * 1.08 * 1.08 << endl;
return 0;
}
Suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) one year, b) two years c) three years
#include <iostream> using namespace std;
int main() {
double balance = 25000.0;
balance = balance * 1.08; cout << "Year 1: $" << balance << endl;
balance = balance * 1.08; cout << "Year 2: $" << balance << endl;
balance = balance * 1.08; cout << "Year 3: $" << balance << endl;
return 0;
}
Suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) one year, b) two years c) three years
#include <iostream>#include <iomanip> using namespace std;
int main() {
cout << fixed << showpoint << setprecision(2); cout << "Year 1: $" << 25000 * 1.08 << endl; cout << "Year 2: $" << 25000 * 1.08 * 1.08 << endl; cout << "Year 3: $" << 25000 * 1.08 * 1.08 * 1.08 << endl;
return 0;
}
Suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) one year, b) two years c) three years
#include <iostream>#include <iomanip> using namespace std;
int main() {
double balance = 25000.0; cout << fixed << showpoint << setprecision(2);
balance = balance * 1.08; cout << "Year 1: $" << balance << endl;
balance = balance * 1.08; cout << "Year 2: $" << balance << endl;
balance = balance * 1.08; cout << "Year 3: $" << balance << endl;
return 0;}
Suppose we alter the program?suppose that I invest $25000 into a mutual
fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirty years
Suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirty years
#include <iostream>#include <iomanip> using namespace std;
int main() {
cout << fixed << showpoint << setprecision(2); cout << "Year 1: $" << 25000 * 1.08 << endl; cout << "Year 2: $" << 25000 * 1.08 * 1.08 << endl; cout << "Year 3: $" << 25000 * 1.08 * 1.08 * 1.08 << endl;
return 0;
}
Suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirty years
#include <iostream>#include <iomanip> using namespace std;
int main() {
cout << fixed << showpoint << setprecision(2); cout << "Year 1: $" << 25000 * 1.08 << endl; cout << "Year 2: $" << 25000 * 1.08 * 1.08 << endl; cout << "Year 3: $" << 25000 * 1.08 * 1.08 * 1.08 << endl;
return 0;
}
Suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirty years
#include <iostream>#include <iomanip> using namespace std;
int main() {
cout << fixed << showpoint << setprecision(2); cout << "Year 10: $" << 25000 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 << endl; cout << "Year 2: $" << 25000 * 1.08 * 1.08 << endl; cout << "Year 3: $" << 25000 * 1.08 * 1.08 * 1.08 << endl;
return 0;
}
Suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirty years
Suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirty years
#include <iostream>#include <iomanip> using namespace std;
int main() {
cout << fixed << showpoint << setprecision(2); cout << "Year 10: $" << 25000 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 << endl; cout << "Year 20: $" << 25000 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 << endl; cout << "Year 30: $" << 25000 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 << endl;
return 0;
}
Suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirty years#include <iostream>#include <iomanip> using namespace std;
int main() {
double balance = 25000.0; cout << fixed << showpoint << setprecision(2);
balance = balance * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08; cout << "Year 10: $" << balance << endl;
balance = balance * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08; cout << "Year 20: $" << balance << endl;
balance = balance * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08; cout << "Year 30: $" << balance << endl;
return 0;}
The previous example worked, but … to calculate 1.0830 required that we manually
type in thirty multiplicationssuppose we had wanted to know the
balance after 100 years?
pow(b,e) to compute b raised to the power of e, one can use
the pow function syntax:
the pow statement itself is an expression value: the first expression raised to the power of the
second expression
pow( , )numericexpression
numeric expression
Example:#include <iostream>#include <cmath> using namespace std; int main() {
cout << pow(3.0, 3.0) << endl; cout << pow(3, 4.0) << endl; cout << pow(4.0, 3) << endl; int x = 5; double y = 6.0; cout << pow(x, y) << endl; cout << pow(x, y) + pow(3.0, 3.0) << endl; cout << pow( pow(x, y), pow(3.0, 3.0) ) << endl; return 0;
}
A note about powyou cannot send it two integer expressions
cout << pow(3, 4) << endl; // compiler error
this has to do with function overloadingwe will examine functions later
for now, just know that one expression has to be a floating point type
The cmath libraryFunction Descriptionabs(x) Returns the absolute value of x
pow(x, y) Returns xy
sqrt(x) Returns the square root of x
sin(x) Returns the sine of x
cos(x) Returns the cosine of x
tan(x) Returns the tangent of x
log(x) Returns the natural logarithm of x ln x
log10(x) Returns log10 x
exp(x) Returns ex
floor(x) Returns the closest whole number < x
ceil(x) Returns the closest whole number > x
A Note about Types when using a math function (from previous slide), the type of
the expression is the same as the type of the input expression, with some exceptions:
an integer expression is converted to a double for the pow function, the type of the expression is the largest of
the base and exponent expressions for abs
integers are not converted to doubles shorts and chars are converted to ints
Expression Type
sqrt(2.0) double
sin(2.0f) float
cos(2) double
log(3 + 4.0f) float
exp(2) + exp(2.0) double
abs(75); int
floor(3.5); double
A Note about the Trig Functions the input expression is considered to be
radians
hence, sin(30.0) = -0.988032, not 0.5
to convert radians to degrees, multiply the value by (π / 180)
Example:#include <iostream>#include <cmath> using namespace std; int main() {
const double PI = 3.14159;
cout << sin(30) << endl;
cout << sin(30 * PI / 180) << endl; return 0;
}
Back to our previous examplesuppose that I invest $25000 into a mutual
fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirty years
Suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirty years
Suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirty years
#include <iostream>#include <iomanip> using namespace std;
int main() {
cout << fixed << showpoint << setprecision(2); cout << "Year 10: $" << 25000 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 << endl; cout << "Year 20: $" << 25000 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 << endl; cout << "Year 30: $" << 25000 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 << endl;
return 0;
}
Suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirty years
Suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirty years
#include <iostream>#include <cmath>#include <iomanip> using namespace std;
int main() {
cout << fixed << showpoint << setprecision(2); cout << "Year 10: $" << 25000 * pow(1.08, 10) << endl; cout << "Year 10: $" << 25000 * pow(1.08, 20) << endl; cout << "Year 10: $" << 25000 * pow(1.08, 30) << endl;
return 0;
}
Suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirty years#include <iostream>#include <iomanip> using namespace std;
int main() {
double balance = 25000.0; cout << fixed << showpoint << setprecision(2);
balance = balance * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08; cout << "Year 10: $" << balance << endl;
balance = balance * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08; cout << "Year 20: $" << balance << endl;
balance = balance * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08 * 1.08; cout << "Year 30: $" << balance << endl;
return 0;}
Suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirty years#include <iostream>#include <cmath>#include <iomanip> using namespace std;
int main() {
double balance = 25000.0; cout << fixed << showpoint << setprecision(2);
balance = balance * pow(1.08, 10); cout << "Year 10: $" << balance << endl;
balance = balance * pow(1.08, 10); cout << "Year 20: $" << balance << endl;
balance = balance * pow(1.08, 10); cout << "Year 30: $" << balance << endl;
return 0;}
Suppose that I invest $25000 into a mutual fund that returns 8% per year. Write a program to calculate how much the fund will be worth after a) ten years, b) twenty years c) thirty years#include <iostream>#include <cmath>#include <iomanip> using namespace std;
int main() {
double balance = 25000.0; double increase = pow(1.08, 10); cout << fixed << showpoint << setprecision(2);
balance = balance * increase; cout << "Year 10: $" << balance << endl;
balance = balance * increase; cout << "Year 20: $" << balance << endl;
balance = balance * increase; cout << "Year 30: $" << balance << endl; return 0;}
Example 2: Suppose you have a cannon. Given an initial velocity of a cannonball and the angle of the cannon θ, output (1) the time that the ball remains in the air and (2) the maximum height of its trajectory
Arithmetic Data and Operators
Given a value θ and initial velocity v0, we can calculate the time that the ball stays in the air:
and its maximum height:
secsin2 0
gvt θ−
=
metersg
vh2
)sin( 20 θ−
=
• g is approximately -9.81 m/s at sea level
Write a program that accepts an initial velocity and the angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places.#include <iostream>#include <cmath>#include <iomanip> using namespace std;
int main() {
const double PI = 3.14159; const double G = -9.81;
double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0;}
Write a program that accepts an initial velocity and the angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places.#include <iostream>#include <cmath>#include <iomanip> using namespace std;
int main() {
const double PI = 3.14159; const double G = -9.81;
double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0;}
Write a program that accepts an initial velocity and the angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places.#include <iostream>#include <cmath>#include <iomanip> using namespace std;
int main() {
const double PI = 3.14159; const double G = -9.81;
double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0;}
Write a program that accepts an initial velocity and the angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places.#include <iostream>#include <cmath>#include <iomanip> using namespace std;
int main() {
const double PI = 3.14159; const double G = -9.81;
double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0;}
Write a program that accepts an initial velocity and the angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places.#include <iostream>#include <cmath>#include <iomanip> using namespace std;
int main() {
const double PI = 3.14159; const double G = -9.81;
double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0;}
Write a program that accepts an initial velocity and the angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places.#include <iostream>#include <cmath>#include <iomanip> using namespace std;
int main() {
const double PI = 3.14159; const double G = -9.81;
double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0;}
secsin2 0
gvt θ−
=
Write a program that accepts an initial velocity and the angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places.#include <iostream>#include <cmath>#include <iomanip> using namespace std;
int main() {
const double PI = 3.14159; const double G = -9.81;
double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / -9.81; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0;}
secsin2 0
gvt θ−
=
cmathcall
Write a program that accepts an initial velocity and the angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places.#include <iostream>#include <cmath>#include <iomanip> using namespace std;
int main() {
const double PI = 3.14159; const double G = -9.81;
double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / -9.81; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0;}
secsin2 0
gvt θ−
=
MagicNumber
Write a program that accepts an initial velocity and the angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places.#include <iostream>#include <cmath>#include <iomanip> using namespace std;
int main() {
const double PI = 3.14159; const double G = -9.81;
double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0;}
secsin2 0
gvt θ−
=
Expects radians
Write a program that accepts an initial velocity and the angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places.#include <iostream>#include <cmath>#include <iomanip> using namespace std;
int main() {
const double PI = 3.14159; const double G = -9.81;
double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * 3.14159 / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0;}
secsin2 0
gvt θ−
=
MagicNumber
Write a program that accepts an initial velocity and the angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places.#include <iostream>#include <cmath>#include <iomanip> using namespace std;
int main() {
const double PI = 3.14159; const double G = -9.81;
double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0;}
secsin2 0
gvt θ−
=
Write a program that accepts an initial velocity and the angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places.#include <iostream>#include <cmath>#include <iomanip> using namespace std;
int main() {
const double PI = 3.14159; const double G = -9.81;
double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0;}
metersg
vh2
)sin( 20 θ−
=
Write a program that accepts an initial velocity and the angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places.#include <iostream>#include <cmath>#include <iomanip> using namespace std;
int main() {
const double PI = 3.14159; const double G = -9.81;
double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0;}
metersg
vh2
)sin( 20 θ−
=
Write a program that accepts an initial velocity and the angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places.#include <iostream>#include <cmath>#include <iomanip> using namespace std;
int main() {
const double PI = 3.14159; const double G = -9.81;
double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0;}
Write a program that accepts an initial velocity and the angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places.#include <iostream>#include <cmath>#include <iomanip> using namespace std;
int main() {
const double PI = 3.14159; const double G = -9.81;
double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(2); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0;}
Write a program that accepts an initial velocity and the angle of trajectory, and computes the hangtime and the maximum height of the cannonball. Output to three decimal places.#include <iostream>#include <cmath>#include <iomanip> using namespace std;
int main() {
const double PI = 3.14159; const double G = -9.81;
double v0; cout << "Initial velocity (m/s): "; cin >> v0; double theta; cout << "Angle of trajectory (degrees): "; cin >> theta; theta = theta * PI / 180.0; double time = -2 * v0 * sin(theta) / G; double height = -pow(v0 * sin(theta), 2) / (2 * G); cout << fixed << showpoint << setprecision(3); cout << "Hangtime (s): " << time << endl; cout << "Height (m): " << height << endl; return 0;}
