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3.4. Composition

Just as with mathematical functions, C++ functions can be composed, meaning that you use one expression as part of another. For example, you can use any expression as an argument to a function:

double x = cos (angle + pi / 2);

This statement takes the value of pi, divides it by two and adds the result to the value of angle. The sum is then passed as an argument to the cos function.

You can also take the result of one function and pass it as an argument to another:

This program finds the log base e of 10 and raises e to that power. The result of this computation is assigned to x.

#include <iostream> #include <cmath> using namespace std; int main () { double x = exp (log (10.0)); cout << x; }

Q-2: Which of these statements has proper syntax?

• double x = log6 (12);

• log6 is not a built in cmath function, but you could write an implementation for it if you wanted!

• double val = abs (tan (1.57));

• This correctly uses cmath functions!

• double num = exp (cosine (0.86667));

• cosine is not a built in cmath function, but cos is!

• double y = exp (cos (1.047)) + exp (tan (2.094))

• This would be correct if it ended in a semi-colon.

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Q-3: Which of these statements returns the y-component of the unit vector at 330 degrees?

• y = cos(330);

• You must always convert to radians before using sinusoidal functions.

• y = cos(330 * 2 * pi / 360);

• cos will return the x-component.

• y = sin(330);

• You must always convert to radians before using sinusoidal functions.

• y = sin(330 * 2 * pi / 360);

• sin returns the y-component, cos returns the x-component.

• y = tan(330 * 2 * pi / 360);

• tan is not the proper function to use here.

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