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

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

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

A
A
B
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C
C
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a
b
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