vault backup: 2024-11-25 10:16:37

education/math/MATH1060 (trig)/Vectors.md

@@ -3,7 +3,7 @@ A vector is a mathematical concept that denotes direction and magnitude. They're
 
 Vectors are often denoted as a matrix with two rows: $\begin{bmatrix}1 \\2\end{bmatrix}$
 # Component Form
-If $\vec{v}$ is a vector with the initial point $(x_y,\ y_i)$, and a terminal point $(x_t,\ y_t)$, we can express $\vec{v}$ in component form as $\vec{v} = <x_t - 
+If $\vec{v}$ is a vector with the initial point $(x_y,\ y_i)$, and a terminal point $(x_t,\ y_t)$, we can express $\vec{v}$ in component form as $\vec{v} = \langle x_t - x_i,\ y_t, -y_i \rangle$ 
 # Magnitude
 The magnitude of a vector is $|\vec{v}| = \sqrt{a^2 + b^2}$
 
@@ -23,4 +23,11 @@ A vector with a magnitude of 1 is a **unit vector**.
 If $\vec{v}$ is a nonzero vector, the unit vector can be found using the equation $\vec{u} = \dfrac{1}{|\vec{v}|}\vec{v}$ . In other words, to find a unit vector, divide the vector by its magnitude.
 
 # $i$, $j$ Notation
-Every 2d vector has a horizontal component and a vertical component. The horizontal unit vector could be written as $i = < 1, 0 >$, and the vertical unit vector could be written as $j = <0, 1 >$. Every vector can be made up using a combination of these standard unit vectors.
+Every 2d vector has a horizontal component and a vertical component. The horizontal unit vector could be written as $i = \langle 1, 0 \rangle$, and the vertical unit vector could be written as $j = \langle 0, 1 \rangle$ Every vector can be made up using a combination of these standard unit vectors.
+
+# Trigonometric Form
+Given a vector $\vec{v}$ with a magnitude $|\vec{v}|$ and direction $\theta$:
+
+The component form is given as:
+
+$$ \vec{v} = \langle \cos \theta,\ |\vec{v}|\sin\theta \rangle $$