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

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

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

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