961 Additive Inverse :
The additive inverse of 961 is -961.
This means that when we add 961 and -961, the result is zero:
961 + (-961) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 961
- Additive inverse: -961
To verify: 961 + (-961) = 0
Extended Mathematical Exploration of 961
Let's explore various mathematical operations and concepts related to 961 and its additive inverse -961.
Basic Operations and Properties
- Square of 961: 923521
- Cube of 961: 887503681
- Square root of |961|: 31
- Reciprocal of 961: 0.0010405827263267
- Double of 961: 1922
- Half of 961: 480.5
- Absolute value of 961: 961
Trigonometric Functions
- Sine of 961: -0.3215367736758
- Cosine of 961: 0.94689709217748
- Tangent of 961: -0.33956886797106
Exponential and Logarithmic Functions
- e^961: INF
- Natural log of 961: 6.8679744089703
Floor and Ceiling Functions
- Floor of 961: 961
- Ceiling of 961: 961
Interesting Properties and Relationships
- The sum of 961 and its additive inverse (-961) is always 0.
- The product of 961 and its additive inverse is: -923521
- The average of 961 and its additive inverse is always 0.
- The distance between 961 and its additive inverse on a number line is: 1922
Applications in Algebra
Consider the equation: x + 961 = 0
The solution to this equation is x = -961, which is the additive inverse of 961.
Graphical Representation
On a coordinate plane:
- The point (961, 0) is reflected across the y-axis to (-961, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 961 and Its Additive Inverse
Consider the alternating series: 961 + (-961) + 961 + (-961) + ...
The sum of this series oscillates between 0 and 961, never converging unless 961 is 0.
In Number Theory
For integer values:
- If 961 is even, its additive inverse is also even.
- If 961 is odd, its additive inverse is also odd.
- The sum of the digits of 961 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
Enter a number (whole number, decimal, or fraction) to find its additive inverse: