3 Additive Inverse :
The additive inverse of 3 is -3.
This means that when we add 3 and -3, the result is zero:
3 + (-3) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 3
- Additive inverse: -3
To verify: 3 + (-3) = 0
Extended Mathematical Exploration of 3
Let's explore various mathematical operations and concepts related to 3 and its additive inverse -3.
Basic Operations and Properties
- Square of 3: 9
- Cube of 3: 27
- Square root of |3|: 1.7320508075689
- Reciprocal of 3: 0.33333333333333
- Double of 3: 6
- Half of 3: 1.5
- Absolute value of 3: 3
Trigonometric Functions
- Sine of 3: 0.14112000805987
- Cosine of 3: -0.98999249660045
- Tangent of 3: -0.14254654307428
Exponential and Logarithmic Functions
- e^3: 20.085536923188
- Natural log of 3: 1.0986122886681
Floor and Ceiling Functions
- Floor of 3: 3
- Ceiling of 3: 3
Interesting Properties and Relationships
- The sum of 3 and its additive inverse (-3) is always 0.
- The product of 3 and its additive inverse is: -9
- The average of 3 and its additive inverse is always 0.
- The distance between 3 and its additive inverse on a number line is: 6
Applications in Algebra
Consider the equation: x + 3 = 0
The solution to this equation is x = -3, which is the additive inverse of 3.
Graphical Representation
On a coordinate plane:
- The point (3, 0) is reflected across the y-axis to (-3, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 3 and Its Additive Inverse
Consider the alternating series: 3 + (-3) + 3 + (-3) + ...
The sum of this series oscillates between 0 and 3, never converging unless 3 is 0.
In Number Theory
For integer values:
- If 3 is even, its additive inverse is also even.
- If 3 is odd, its additive inverse is also odd.
- The sum of the digits of 3 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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