# angle between

(0.001 seconds)

## 6 matching pages

##### 1: 7.20 Mathematical Applications
Furthermore, because $\ifrac{\mathrm{d}y}{\mathrm{d}x}=\tan\left(\frac{1}{2}\pi t^{2}\right)$, the angle between the $x$-axis and the tangent to the spiral at $P(t)$ is given by $\frac{1}{2}\pi t^{2}$. …
##### 2: 1.9 Calculus of a Complex Variable
###### Conformal Transformation
The angle between $C_{1}$ and $C_{2}$ at $z_{0}$ is the angle between the tangents to the two arcs at $z_{0}$, that is, the difference of the signed angles that the tangents make with the positive direction of the real axis. If $f^{\prime}(z_{0})\not=0$, then the angle between $C_{1}$ and $C_{2}$ equals the angle between $C^{\prime}_{1}$ and $C^{\prime}_{2}$ both in magnitude and sense. …
##### 3: 1.6 Vectors and Vector-Valued Functions
1.6.4 $\cos\theta=\frac{\mathbf{a}\cdot\mathbf{b}}{\left\|{\mathbf{a}}\right\|\;\left% \|{\mathbf{b}}\right\|};$
$\theta$ is the angle between $\mathbf{a}$ and $\mathbf{b}$. …
1.6.9 $\mathbf{a}\times\mathbf{b}=\begin{vmatrix}\mathbf{i}&\mathbf{j}&\mathbf{k}\\ a_{1}&a_{2}&a_{3}\\ b_{1}&b_{2}&b_{3}\end{vmatrix}\\ =(a_{2}b_{3}-a_{3}b_{2})\mathbf{i}+(a_{3}b_{1}-a_{1}b_{3})\mathbf{j}+(a_{1}b_{% 2}-a_{2}b_{1})\mathbf{k}\\ =\left\|{\mathbf{a}}\right\|\left\|{\mathbf{b}}\right\|(\sin\theta)\mathbf{n},$
##### 4: 3.2 Linear Algebra
Because $\left|\mathbf{y}^{\rm T}\mathbf{x}\right|=\left|\cos\theta\right|$, where $\theta$ is the angle between $\mathbf{y}^{\rm T}$ and $\mathbf{x}$ we always have $\kappa(\lambda)\geq 1$. …
##### 5: 31.16 Mathematical Applications
Expansions of Heun polynomial products in terms of Jacobi polynomial (§18.3) products are derived in Kalnins and Miller (1991a, b, 1993) from the viewpoint of interrelation between two bases in a Hilbert space:
31.16.1 $\mathit{Hp}_{n,m}\left(x\right)\mathit{Hp}_{n,m}\left(y\right)=\sum_{j=0}^{n}A% _{j}{\sin}^{2j}\theta\*P^{(\gamma+\delta+2j-1,\epsilon-1)}_{n-j}\left(\cos% \left(2\theta\right)\right)P^{(\delta-1,\gamma-1)}_{j}\left(\cos\left(2\phi% \right)\right),$
##### 6: 2.1 Definitions and Elementary Properties
means that for each $n$, the difference between $f(x)$ and the $n$th partial sum on the right-hand side is $O\left((x-c)^{n}\right)$ as $x\to c$ in $\mathbf{X}$. … For (2.1.14) $\mathbf{X}$ can be the positive real axis or any unbounded sector in $\mathbb{C}$ of finite angle. …