Cosine Similarity
0.71
Angle:
45.0°
Projection of B on A:
0.71
Vector A (unit):
(0.87, 0.50)
Vector B (unit):
(0.31, 0.95)
The Cosine Function
Cosine Similarity Formula
$$\cos(\theta) = \hat{\mathbf{A}} \cdot \hat{\mathbf{B}} = A_x B_x + A_y B_y \qquad \text{(for unit vectors } |\hat{\mathbf{A}}| = |\hat{\mathbf{B}}| = 1\text{)}$$
Current calculation:
$$\cos(\theta) = \hat{\mathbf{A}} \cdot \hat{\mathbf{B}} = (0.87)(0.31) + (0.50)(0.95) = 0.74$$