Cosine of Vector: Adjacent/Hypothenuse

In summary: The cosine function is not defined for vectors. It only applies to angles or numbers. In summary, the statement "The cosine of a vector is equal to the opposite over its magnitude" is incorrect and nonsensical. The cosine function is only defined for angles or numbers, not vectors.
  • #1
Tiven white
58
0

Homework Statement


The cosine of a vector is equal to the opposite over its magnitude.

Homework Equations



The attempt at a solution[/b] the cosine is the ratio of the adjacent to the hypothenuse this is why i say it "came' is incorrect.
 
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  • #2
What exactly was the original question?
 
  • #3
haruspex said:
What exactly was the original question?
That is the ?,its a true or false
 
  • #4
Tiven white said:
That is the ?,its a true or false
What statement is true or false?

Oh, I see. It's this statement that's being questioned:
The cosine of a vector is equal to the opposite over its magnitude.

Yes, it's an incorrect statement, as you pointed out.
 
Last edited:
  • #5
NascentOxygen said:
What statement is true or false?


If the cosine of a vector is its y component over its magnitude?
 
  • #6
It's not the vector which has a cosine. It's only angles which have cosines.
 
  • #7
Tiven white said:

Homework Statement


The cosine of a vector is equal to the opposite over its magnitude.
If this really is the statement, I would not say it was either "true" or "false". I would just say it is non-sense! The function "cosine" is not [g]defined[/b] for vectors, only for angles or numbers. Further, saying "the opposite" is non-sense. "Opposite" is an adjective not a noun and cannot take the article "the".

Homework Equations



The attempt at a solution
the cosine is the ratio of the adjacent to the hypothenuse this is why i say it "came' is incorrect.
 
  • #8
Just out of curiosity, what is
Tiven white said:
this is why i say it "came' is incorrect.
supposed to mean?
 
  • #9
vela said:
Just out of curiosity, what is
[ C A M ]
supposed to mean?

cosine = adjacent ÷ magnitude ?
 
  • #10
Wouldn't that be correct?
 
  • #11
vela said:
Wouldn't that be correct?
Clearly, OP is a little confused.
 
  • #12
cosine

NascentOxygen said:
Clearly, OP is a little confused.


The question was asking whether the statement ' cosine means the y component of a vector over its magnitude'.
Is this true or false?
 
  • #13
Tiven white said:
The question was asking whether the statement ' cosine means the y component of a vector over its magnitude'.
Is this true or false?
Definitely false.
 

Related to Cosine of Vector: Adjacent/Hypothenuse

What is the definition of cosine of a vector?

The cosine of a vector is a mathematical function that calculates the ratio of the adjacent side of a right triangle to its hypotenuse. It is commonly used in trigonometry to determine the angle between a vector and the horizontal axis.

How do you calculate the cosine of a vector?

The cosine of a vector can be calculated by dividing the length of the adjacent side of the triangle by the length of the hypotenuse. This can be represented by the formula cos(theta) = adjacent/hypotenuse.

What is the relationship between the cosine of a vector and the angle of a triangle?

The cosine of a vector is equal to the cosine of the angle formed between the vector and the horizontal axis. This means that the value of the cosine of a vector is dependent on the angle of the triangle.

What is the range of values for the cosine of a vector?

The cosine of a vector can range from -1 to 1. A value of -1 indicates that the vector is perpendicular to the horizontal axis, a value of 0 indicates that the vector is parallel to the horizontal axis, and a value of 1 indicates that the vector is in the same direction as the horizontal axis.

How is the cosine of a vector used in real-world applications?

The cosine of a vector is used in various fields such as physics, engineering, and computer graphics. It is used to calculate forces, angles, and projections in real-world scenarios. It is also used in navigation and satellite tracking systems.

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