Mathematical Library Methods Quiz

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Questions and Answers

What is the output of the statement 'System.out.println("Result of min value = " + n);' when n is assigned the value from Math.min(4, 8)?

Result of min value = 4 (correct)

Result of min value = 8

Result of min value = 12

No output due to an error

Which of the following statements is true about the Math.max() function for negative numbers?

Math.max() always returns the positive value.

Math.max() returns the less negative number. (correct)

Math.max() will return the smaller absolute value.

Math.max() does not work with negative numbers.

What is the type of variable that will store the result from the statement 'double n=Math.min(4.8, 2.8);'?

int

double (correct)

float

long

What will be the output of the statement for n when assigned from Math.min(-3.5, -9.5)?

Result of min value = -9.5 Signup and view all the answers

Which of the following correctly represents the output format for a Math.max() function?

Math.max() returns the input that is greater. Signup and view all the answers

What does the Math.min() function return?

The minimum of two numbers Signup and view all the answers

What will the following code return: double x = Math.min(-3.5, -9.5);?

-9.5 Signup and view all the answers

Which method would be used to find the maximum value between two double numbers?

Math.max() Signup and view all the answers

If Math.max(4, 8) is called, what will be the returned data type?

int Signup and view all the answers

What will Math.abs(-7.5) return?

7.5 Signup and view all the answers

Which function is used to compute the square root of a number?

Math.sqrt() Signup and view all the answers

If you need to convert an angle from degrees to radians, which approach should you apply?

Multiply by $rac{ ext{π}}{180}$ Signup and view all the answers

What is the output of Math.sin(90 degrees) in Java if degrees are first converted to radians?

1 Signup and view all the answers

What will be the output of `Math.round(14.49)`?

14.0 Signup and view all the answers

What does the `Math.rint()` function return when called with a negative number?

The nearest integer in double data type Signup and view all the answers

If you execute `Math.round(-12.51)`, what will be the result?

-13.0 Signup and view all the answers

After running the sample program, what is the value of variable `n`?

15.0 Signup and view all the answers

How does `Math.round()` treat a fractional part that equals exactly 0.5?

It rounds up to the nearest integer. Signup and view all the answers

What is the output of the statement `Math.cbrt(3375)` in the provided sample program?

15.0 Signup and view all the answers

Which of the following functions returns the natural logarithm of a number?

Math.log() Signup and view all the answers

What result would `Math.round(12.3)` generate in a Java program?

12 Signup and view all the answers

If `double d=Math.abs(-9.99);` is executed, what value will `d` hold?

9.99 Signup and view all the answers

Which method would you use to round a number to the nearest integer?

Math.round() Signup and view all the answers

What does `Math.cbrt(-3.375)` output?

-1.5 Signup and view all the answers

What will `Math.log(6.25)` return in terms of type and value?

double, 1.8325814638827256 Signup and view all the answers

What is the correct syntax for using the Math.abs() function?

Math.abs(number); Signup and view all the answers

How can you generate a random integer between 5 and 10 using the random function in Java?

int r = (int)(Math.random()*6) + 5; Signup and view all the answers

What is the correct mathematical relationship to convert degrees to radians?

radians = degrees * (π/180) Signup and view all the answers

What range of values can the variable n take when using 'int n = (int)(Math.random()*2);'?

0 and 1 Signup and view all the answers

Which method can directly convert an angle from degrees to radians in Java without manual calculations?

Math.toRadians() Signup and view all the answers

If the degrees variable is assigned a value of 180, what will be the approximate value of radians when using 'radians = Math.PI/180 * degrees'?

1.57 Signup and view all the answers

What will be the output of the program that calculates the angle for a sine ratio of 0.5, after converting the angle from radians to degrees?

30 degrees Signup and view all the answers

What does the Math.acos function return when provided with an argument of 0.5?

45 radians Signup and view all the answers

When converting radians to degrees, which mathematical relation is used in the sample program?

degrees = radians * 180/π Signup and view all the answers

In the execution of the program that computes the cosine of 0.5, what will the rounded result of the degree conversion be?

60 degrees Signup and view all the answers

What result will the Math.asin function provide when it receives an argument of 1?

π/2 radians Signup and view all the answers

What does the Math.log() function return when called with a positive number?

A double type value Signup and view all the answers

What will be the output of Math.round(-8.49)?

-8 Signup and view all the answers

Which of the following inputs to Math.abs() will return a value of 9.99?

-9.99 Signup and view all the answers

What is the result of Math.round(8.5)?

9 Signup and view all the answers

What will Math.log(-5) return?

An undefined value Signup and view all the answers

If you input the value -10 to the Math.abs() function, what will be the output?

10 Signup and view all the answers

Which statement is true regarding Math.round() when applied to negative numbers?

It behaves differently depending on the fractional part. Signup and view all the answers

Which function can be used to obtain the magnitude of -7.3?

Math.abs() Signup and view all the answers

What will Math.sqrt(-16) return?

NaN Signup and view all the answers

If you execute `double z = Math.sqrt(25.0);`, what is the value assigned to z?

5.0 Signup and view all the answers

In the provided example, what does the output 'Result of square root of a negative no.=NaN' signify?

The function encountered an invalid input. Signup and view all the answers

What data type is returned by the Math.sqrt() function?

Double Signup and view all the answers

In the sample program, what is printed as the value for `n` after executing `Math.sqrt(184.25)`?

13.5738719604498227 Signup and view all the answers

What is the output of the statement 'double n = Math.sqrt(16.0);'?

4.0 Signup and view all the answers

What value does Math.sqrt(-3.0) return in Java?

NaN Signup and view all the answers

Which function is used to calculate the exponential value of a number in Java?

Math.pow() Signup and view all the answers

What is the result of executing 'double d = Math.pow(5.0, -2.0);'?

0.04 Signup and view all the answers

How is the result of Math.sqrt() expressed in Java?

As a double type value. Signup and view all the answers

Which of the following numbers will produce a valid result using Math.sqrt()?

0.0 Signup and view all the answers

What would the value of 'm' be in 'double m = Math.sqrt(6.25);'?

2.5 Signup and view all the answers

In the statement 'double d = Math.pow(2.0, 3.0);', what value is assigned to d?

8.0 Signup and view all the answers

How can you convert an angle from radians to degrees using a mathematical relation?

degree = (radian * 180)/Math.PI Signup and view all the answers

What is the purpose of the Math.toDegrees() function in Java?

To convert radians to degrees Signup and view all the answers

Which Java command is used to find the cosine of an angle?

Math.cos() Signup and view all the answers

What must be done to an angle in degrees before using Java's trigonometric functions?

Convert it to radians Signup and view all the answers

In the provided Java code, what is the value of 'd' calculated as?

Cosine of 60 degrees Signup and view all the answers

Which mathematical concept is utilized to convert angles from degrees to radians in Java?

Multiply by π and divide by 180 Signup and view all the answers

What is the correct syntax for using the sine function in Java?

double val = Math.sin(angle); Signup and view all the answers

What would be the output of the 'System.out.println' statement in the sample program for cosine?

0.86602540378 Signup and view all the answers

Study Notes

Mathematical Library Methods Overview

Java provides built-in mathematical library methods within the Math class, part of the java.lang package.
These methods facilitate various mathematical operations widely used in programming.

Key Math Functions

Math.min(x, y): Returns the smaller of two numbers, maintaining the data type of the arguments.
Math.max(x, y): Returns the larger of two numbers, also preserving the data type.
Math.sqrt(x): Returns the square root of a positive number as a double. Returns NaN for negative inputs.
Math.pow(x, y): Computes x raised to the power of y, returning the result as a double.
Math.abs(x): Returns the absolute value of a number, maintaining the respective data type.

Special Cases of Math Functions

Math.cbrt(x): Calculates the cube root of a number, returning a double for positive or negative inputs.
Math.log(x): Computes the natural logarithm of x, returning a double type value.
Math.round(x): Rounds x to the nearest integer, returning a long or int. Rounding behaviors differ for positive and negative numbers.

Random Number Generation

Math.random(): Generates a random double between 0.0 (inclusive) and 1.0 (exclusive).
To obtain a random integer between 1 and n: int r = (int)(Math.random() * n) + 1;
For a range between m and n: int r = (int)((Math.random() * (n - m)) + m);

Angle Conversion Methods

Degrees to Radians: Convert using Math.toRadians(degree) or radian = degree * (Math.PI / 180).
Radians to Degrees: Convert using Math.toDegrees(radian) or degree = radian * (180 / Math.PI).

Trigonometric Functions

Functions include Math.sin(angle), Math.cos(angle), and Math.tan(angle); these assume the input is in radians.
To find an angle using a known trigonometric ratio, use arc functions: Math.asin(value), Math.acos(value), and Math.atan(value).

Usage Examples

The minimum and maximum functions can be demonstrated with:

int n = Math.min(4, 6); // Returns 4
double m = Math.max(3.4, 8.9); // Returns 8.9

Square root calculation:

double sqrtValue = Math.sqrt(25); // Returns 5.0

Power calculation:

double powerValue = Math.pow(2, 3); // Returns 8.0

Noteworthy Considerations

Square roots of negative numbers return NaN: Math.sqrt(-1) results in NaN.
Absolute function always results in a non-negative number regardless of input sign.
Rounding method considerations depend on the fractional part of the number.

Example Programs

To find a cosine value from a given degree:

double rad = Math.toRadians(60); // Converts 60 degrees to radians
double cosValue = Math.cos(rad);

To find an angle from a sine ratio:

double angleInRadians = Math.asin(0.5); // Returns sine inverse
double angleInDegrees = Math.toDegrees(angleInRadians);

Summary

Understanding these mathematical library methods in Java enhances computational abilities, allowing precision and efficiency in programming.

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Description

Test your knowledge on various methods of the Math class, including power, square root, and trigonometric functions. Explore the behavior of numbers in these functions and practice angle conversions between degrees and radians. This quiz will reinforce your understanding of essential mathematical concepts used in programming.