# Mathematics Advanced: Trigonometric Functions

Table of Contents

## Radians

• Radians are a fundamental component of year 11 and 12 Trigonometry
• They are another unit for angle, like degrees
• They can be calculated from degrees using the following formula:

$$\color{lightblue}{Radians = Degrees\cdot \frac{180}{\pi}}$$

$$\color{lightblue}{Degrees = Radians\cdot \frac{\pi}{180}}$$

### Radians Mnemonic

• Here’s an easy way to remember radians conversions:
$$sin(0)$$ $sin(0^\circ)$ $\frac{\sqrt{0}}{2}$ $cos(90^\circ)$ $cos\frac{\pi}{2}$
$$sin(\frac{\pi}{6})$$ $sin(30^\circ)$ $\frac{\sqrt{1}}{2}$ $cos(60^\circ)$ $cos\frac{\pi}{3}$
$$sin(\frac{\pi}{4})$$ $sin(45^\circ)$ $\frac{\sqrt{2}}{2}$ $cos(45^\circ)$ $cos\frac{\pi}{4}$
$$sin(\frac{\pi}{3})$$ $sin(60^\circ)$ $\frac{\sqrt{3}}{2}$ $cos(30^\circ)$ $cos\frac{\pi}{6}$
$sin(\frac{\pi}{2})$ $sin(90^\circ)$ $\frac{\sqrt{4}}{2}$ $cos(0^\circ)$ $cos(0)$
⬆ The number in the square root: 0, 1, 2, 3, 4

## Sine and Cosine Rule

### Sine Rule

$$\color{lightblue}{\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}}$$

### Cosine Rule

Sides: $${\color{Red} a}{\color{Cyan} =\sqrt{{\color{Red} b}^2 +{\color{Red} c}^2 -2{\color{Red} bc}\cdot cos{\color{Green} A}}}$$

Angles: $${\color{Green} A}{\color{Cyan} =cos^{-1}\frac{{\color{Red} b}^2 + {\color{Red} c}^2 -{\color{Red} a}^2}{2{\color{Red} bc}}}$$

##### Pranav Sharma
###### Site Owner

Year 12 Student, site owner and developer.

##### Jackson Taylor
###### Post Writer

I’m a Year 12 student at Sydney Tech.