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