8 Additive Inverse :
The additive inverse of 8 is -8.
This means that when we add 8 and -8, the result is zero:
8 + (-8) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 8
- Additive inverse: -8
To verify: 8 + (-8) = 0
Extended Mathematical Exploration of 8
Let's explore various mathematical operations and concepts related to 8 and its additive inverse -8.
Basic Operations and Properties
- Square of 8: 64
- Cube of 8: 512
- Square root of |8|: 2.8284271247462
- Reciprocal of 8: 0.125
- Double of 8: 16
- Half of 8: 4
- Absolute value of 8: 8
Trigonometric Functions
- Sine of 8: 0.98935824662338
- Cosine of 8: -0.14550003380861
- Tangent of 8: -6.7997114552204
Exponential and Logarithmic Functions
- e^8: 2980.9579870417
- Natural log of 8: 2.0794415416798
Floor and Ceiling Functions
- Floor of 8: 8
- Ceiling of 8: 8
Interesting Properties and Relationships
- The sum of 8 and its additive inverse (-8) is always 0.
- The product of 8 and its additive inverse is: -64
- The average of 8 and its additive inverse is always 0.
- The distance between 8 and its additive inverse on a number line is: 16
Applications in Algebra
Consider the equation: x + 8 = 0
The solution to this equation is x = -8, which is the additive inverse of 8.
Graphical Representation
On a coordinate plane:
- The point (8, 0) is reflected across the y-axis to (-8, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 8 and Its Additive Inverse
Consider the alternating series: 8 + (-8) + 8 + (-8) + ...
The sum of this series oscillates between 0 and 8, never converging unless 8 is 0.
In Number Theory
For integer values:
- If 8 is even, its additive inverse is also even.
- If 8 is odd, its additive inverse is also odd.
- The sum of the digits of 8 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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