Find the sin angle between two 2d vectors

In summary, The conversation is about finding the missing angle theta between two vectors, U=<1,3> and V=<5,2>, for both cos(theta) and sin(theta). The speaker knows how to find the missing angle for cos(theta) but not for sin(theta), and is asking for the formula and a step by step explanation. They also mention that a Pythagorean identity can be used once cos(theta) is known.
  • #1
Elissa89
52
0
Tomorrow is my math test and I'm going over the study guide:

I have vector U=<1, 3> and vector V=<5, 2>

It says let theta be the missing angle between the two vectors. What is the cos(theta) and sin(theta)?

I already know how to find the missing angle for cos(theta) but we never covered how to find the missing angle for sin(theta). It was never in our homework and it's not in my notes but apparently it could be on the test.

So if someone could give me the formula and then show a step by step on how to do this it would be most appreciated.
 
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  • #2
Once you know \(\cos(\theta)\), then given \(0\le\theta\le\pi\), we may use a Pythagorean identity:

\(\displaystyle \sin(\theta)=\sqrt{1-\cos^2(\theta)}\)
 

1. What is the formula for finding the sine angle between two 2d vectors?

The formula for finding the sine angle between two 2d vectors is:
sin(θ) = (a x b) / (|a| * |b|)
Where a and b are the two vectors and θ is the angle between them.

2. How do I find the magnitude of a vector?

The magnitude of a vector can be found by taking the square root of the sum of the squares of its components. For example, if a vector is represented as (x, y), its magnitude would be √(x² + y²).

3. What is the significance of finding the sine angle between two vectors?

Finding the sine angle between two vectors can help determine the direction and magnitude of the rotational force needed to align one vector with the other. It is also useful in calculating the work done by a force on an object.

4. Can the sine angle between two vectors be negative?

Yes, the sine angle between two vectors can be negative. This indicates that the two vectors are in opposite directions.

5. How do I interpret the value of the sine angle between two vectors?

The value of the sine angle between two vectors ranges from -1 to 1. A value of 1 indicates that the two vectors are parallel and in the same direction, while a value of -1 indicates that they are parallel but in opposite directions. A value of 0 means the two vectors are perpendicular to each other. Any other value between -1 and 1 signifies the degree of alignment between the two vectors.

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