MHB Find the angle between 2 vectors w=i+3j, vector v=<5, 2>

Click For Summary
To find the angle between vectors w = i + 3j and v = <5, 2>, first calculate the cosine of the angle using the dot product formula. The cosine can be derived from the formula cos(θ) = (w · v) / (||w|| ||v||). Once the cosine is determined, the sine can be found using the Pythagorean identity sin(θ) = √(1 - cos²(θ)). This method allows for the complete determination of the angle between the two vectors. Understanding both sine and cosine is essential for solving problems involving vector angles.
Elissa89
Messages
52
Reaction score
0
I know how to find the cos(theta) between two vectors but I do not know how to find the sin(theta).

vector w=i+3j

vector v=<5, 2>
 
Mathematics news on Phys.org
Elissa89 said:
I know how to find the cos(theta) between two vectors but I do not know how to find the sin(theta).

vector w=i+3j

vector v=<5, 2>

find the cosine, then use a form of the Pythagorean identity ...

$\sin{t} = \sqrt{1-\cos^2{t}}$
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

Undergrad Are There Other Ways To Represent Vectors Besides Arrows?
  • · Replies 9 ·
Replies
9
Views
2K
MHB What is the Angle Between Vectors Using the Dot Product Formula?
  • · Replies 4 ·
Replies
4
Views
1K
MHB Find the sin angle between two 2d vectors
  • · Replies 1 ·
Replies
1
Views
2K
Preservation of the angle between two vectors
  • · Replies 9 ·
Replies
9
Views
2K
High School Confusion about the angle between two vectors in a cross product
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Transforming coordinates between Cartesian and spherical
  • · Replies 1 ·
Replies
1
Views
2K
High School To calculate the polar unit vectors using rotated coordinates
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Converting this vector into polar form
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Is it valid to express a complex number as a vector?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Angles between 4-vectors in special relativity?
  • · Replies 5 ·
Replies
5
Views
1K