Chapter 4, Problem 1CP

a.

Explanation of Solution

Given: The value of PI is 3.14159 and E has the value 2.71828.

To find: That what will be the result of the function, sqrt(4.0).

Solution:

The function, sqrt(4.0), will evaluate to 2. The sqrt function will perform the square root of the number which is passed in the function parameter. It is a library function belonging to the header, cmath.

b.

Explanation of Solution

Given: The value of PI is 3.14159 and E has the value 2.71828.

To find: That what will be the result of the function, sin(2*PI).

Solution:

The function, sin(2*PI) , evaluates to 0. The sin function returns the final value of the sine of the angle which is passed in the parameter. It is a library function belonging to the header, cmath. It returns the sine of angle in radians.

c.

Explanation of Solution

Given: The value of PI is 3.14159 and E has the value 2.71828.

To find: That what will be the result of the function, cos(2*PI).

Solution:

The function, cos(2*PI), evaluates to 1. The cosine function returns the final value of the cosine of the angle which is passed in the parameter. It is a library function belonging to the header, cmath. It returns the cosine of angle in radians.

d.

Explanation of Solution

Given: The value of PI is 3.14159 and E has the value 2.71828.

To find: That what will be the result of the function, pow(2.0, 2).

Solution:

The function, pow(2.0, 2), will return the value 4. It computes the base number which is raised to the power of the exponent number. It is a library function belonging to the header, cmath. It follows the syntax pow(base, exponent).

e.

Explanation of Solution

Given: The value of PI is 3.14159 and E has the value 2.71828.

To find: That what will be the result of the function, log(E).

Solution:

The function, log(E), will evaluate to 1. It returns the natural logarithmic value of the argument which is passed as the parameter. The parameters can belong to any data type, like int, float, double or long-double.

f.

Explanation of Solution

Given: The value of PI is 3.14159 and E has the value 2.71828.

To find: That what will be the result of the function, exp(1.0).

Solution:

The function, exp(1.0), will return the value 2. It returns the exponential, e, which is raised to the argument that is given. It is a library function belonging to the header, cmath.

g.

Explanation of Solution

Given: The value of PI is 3.14159 and E has the value 2.71828.

To find: That what will be the result of the function, max(2, min(3, 4)).

Solution:

The function, max(2, min(3,4)), will return the value 3. The min function returns the minimum of the parameters passed to the function. Whereas, the max function returns the maximum of the parameters passed. In the given condition, first the inner bracket will evaluate, so the min(3,4) will be 3. Then, the outer bracket will evaluate, so the max(2,3) will be 3. Thereby, making the final result to be 3.

h.

Explanation of Solution

Given: The value of PI is 3.14159 and E has the value 2.71828.

To find: That what will be the result of the function, sqrt(125.0).

Solution:

The function, sqrt(125.0), will evaluate to 11. The sqrt function is the function which helps in finding the square root of the parameter which is passed to the function. It is a library function belonging to the header, cmath.

i.

Explanation of Solution

Given: The value of PI is 3.14159 and E has the value 2.71828.

To find: That what will be the result of the function, ceil(-2.5).

Solution:

The function, ceil(-2.5), will return the value -2.0. It returns the smallest possible value which has to be either greater than or equal to the passed argument. It is a library function belonging to the header, cmath.

j.

Explanation of Solution

Given: The value of PI is 3.14159 and E has the value 2.71828.

To find: That what will be the result of the function, floor(-2.5).

Solution:

The function, floor(-2.5), will return the value -3.0. It will return the largest possible value which has to be either equal to or less than the passed argument. It is a library function belonging to the header, cmath.

k.

Explanation of Solution

Given: The value of PI is 3.14159 and E has the value 2.71828.

To find: That what will be the result of the function, asin(0.5).

Solution:

The function, asin(0.5), will return the value 0.52359. It returns the inverse of the sine of the angle which is passed as the parameter. It returns the value of the angle in radians. It is a library function belonging to the header, cmath.

l.

Explanation of Solution

Given: The value of PI is 3.14159 and E has the value 2.71828.

To find: That what will be the result of the function, acos(0.5).

Solution:

The function, acos(0.5), will return the value 1.04719. It returns the inverse of the cosine of the angle which is passed as the parameter. It returns the value of the angle in radians. It is a library function belonging to the header, cmath.

m.

Explanation of Solution

Given: The value of PI is 3.14159 and E has the value 2.71828.

To find: That what will be the result of the function, atan(1.0).

Solution:

The function, atan(1.0), will return the value 0.785398. It returns the inverse of the tangent of the angle which is passed as the parameter. It returns the value of the angle in radians. It is a library function belonging to the header, cmath.

n.

Explanation of Solution

Given: The value of PI is 3.14159 and E has the value 2.71828.

To find: That what will be the result of the function, ceil(2.5).

Solution:

The function, ceil(2.5), will return the value 3.0. It returns the smallest possible value which has to be either greater than or equal to the passed argument. It is a library function belonging to the header, cmath.

o.

Explanation of Solution

Given: The value of PI is 3.14159 and E has the value 2.71828.

To find: That what will be the result of the function, floor(2.5).

Solution:

The function floor, (2.5), will return the value 2.0. It will return the largest possible value which has to be either lesser than or equal to the passed argument. It is a library function belonging to the header, cmath.

p.

Explanation of Solution

Given: The value of PI is 3.14159 and E has the value 2.71828.

To find: That what will be the result of the function, log10(10.0).

Solution:

The function, log10(10.0), will return the value of 1. It returns the common base 10 logarithmic value of the argument which is passed inside. It is a library function belonging to the header, cmath.

q.

Explanation of Solution

Given: The value of PI is 3.14159 and E has the value 2.71828.

To find: That what will be the result of the function, pow(2.0, 3).

Solution:

The function, pow(2.0, 3), will return the value 8.0. It computes the base number which is raised to the power of the exponent number. It is a library function belonging to the header, cmath. It follows the syntax, pow(base, exponent).