Mathematics Advanced: Trigonometric Functions

Last updated on August 24, 2021 1 min read Year 11, Mathematics Advanced

Table of Contents

Radians

$R a d i a n s = D e g r e e s \cdot \frac{180}{π}$
$D e g r e e s = R a d i a n s \cdot \frac{π}{180}$

$s i n (0)$	$s i n (0^{\circ})$	$\frac{\sqrt{0}}{2}$	$c o s (90^{\circ})$	$c o s \frac{π}{2}$
$s i n (\frac{π}{6})$	$s i n (30^{\circ})$	$\frac{\sqrt{1}}{2}$	$c o s (60^{\circ})$	$c o s \frac{π}{3}$
$s i n (\frac{π}{4})$	$s i n (45^{\circ})$	$\frac{\sqrt{2}}{2}$	$c o s (45^{\circ})$	$c o s \frac{π}{4}$
$s i n (\frac{π}{3})$	$s i n (60^{\circ})$	$\frac{\sqrt{3}}{2}$	$c o s (30^{\circ})$	$c o s \frac{π}{6}$
$s i n (\frac{π}{2})$	$s i n (90^{\circ})$	$\frac{\sqrt{4}}{2}$	$c o s (0^{\circ})$	$c o s (0)$
		⬆ The number in the square root: 0, 1, 2, 3, 4

$\frac{s i n (A)}{a} = \frac{s i n (B)}{b} = \frac{s i n (C)}{c}$

Sides: $a = \sqrt{b^{2} + c^{2} - 2 b c \cdot c o s A}$
Angles: $A = c o s^{- 1} \frac{b^{2} + c^{2} - a^{2}}{2 b c}$