Multiplication with modulus of function

In summary, the question is asking if |Cos(theta)|*Cos(theta) is equal to Cos^(theta) and if only positive values of Cos(theta) are considered. However, this depends on whether or not the value of Cos(theta) is positive or negative, as |a|*a is equal to a^2 for non-negative values and -a^2 for negative values.
  • #1
Silva_physics
10
0
Hi!
Could anybody, please, tell me:
whether |Cos(theta)|*Cos(theta) = Cos^(theta) , because it means that only positive values of Cos(theta) are taken.
Am I right?:shy:
 
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  • #2
= Cos^2(theta)
 
  • #3
Silva_physics said:
Hi!
Could anybody, please, tell me:
whether |Cos(theta)|*Cos(theta) = Cos^(theta) , because it means that only positive values of Cos(theta) are taken.
Am I right?:shy:
That's not a well phrased question. |Cos(theta)| is necessarily positive but the "Cos(theta)" outside the "modulus" is not so resticted.

In general |a|*a is equal to [itex]a^2[/itex] if a is non-negative, but equal to [itex]-a^2[/itex] if a is negative.
 
  • #4
Thanks:wink:
 
  • #5


Hello! That's a great question. The answer is yes, you are correct. When you multiply a function by its modulus, you are essentially taking the absolute value of that function. In the case of cos(theta), this means that only positive values of cos(theta) will be used in the multiplication. So, the result of |cos(theta)|*cos(theta) will be equivalent to cos^2(theta), as you mentioned. This can be seen graphically by looking at the graph of cos(theta), which only has positive values. I hope this helps clarify things for you!
 

Related to Multiplication with modulus of function

1. What is the purpose of multiplication with modulus of function?

Multiplication with modulus of function is used to calculate the remainder when dividing a number by another number. It is often used in cryptography and coding to ensure the security and accuracy of calculations.

2. How does multiplication with modulus of function work?

Multiplication with modulus of function involves multiplying two numbers together and then finding the remainder when dividing the result by a third number, known as the modulus. This can be represented mathematically as (a * b) % c, where a and b are the two numbers being multiplied and c is the modulus.

3. What is the difference between multiplication with modulus of function and regular multiplication?

The main difference between the two is that regular multiplication produces a result that is the exact product of the two numbers being multiplied, while multiplication with modulus of function produces the remainder when dividing that product by a third number. This means that the result of multiplication with modulus of function is always less than the third number (modulus).

4. Can multiplication with modulus of function be applied to all numbers?

Yes, multiplication with modulus of function can be applied to all numbers, including whole numbers, fractions, and even negative numbers. However, the result may vary depending on the numbers being multiplied and the modulus used.

5. What are some real-world applications of multiplication with modulus of function?

Multiplication with modulus of function is commonly used in cryptography and coding to ensure the accuracy and security of calculations. It is also used in mathematics to find patterns in numbers and to solve equations involving remainders.

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