Trigonometry

CHAPTER 6

6.1

Trigonometric Ratios (SOH CAH TOA)

Ratio	Definition	Memory
$\sin\theta$	$\dfrac{\text{Opposite}}{\text{Hypotenuse}}$	SOH
$\cos\theta$	$\dfrac{\text{Adjacent}}{\text{Hypotenuse}}$	CAH
$\tan\theta$	$\dfrac{\text{Opposite}}{\text{Adjacent}}$	TOA

6.2

Special Angles

Angle	$\sin$	$\cos$	$\tan$
$30°$	$\frac{1}{2}$	$\frac{\sqrt{3}}{2}$	$\frac{1}{\sqrt{3}}$
$45°$	$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{2}}{2}$	$1$
$60°$	$\frac{\sqrt{3}}{2}$	$\frac{1}{2}$	$\sqrt{3}$

6.3

Sine Rule & Cosine Rule

Sine Rule

$\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$

Cosine Rule

$a^2 = b^2 + c^2 - 2bc\cos A$

Given	Use
AAS / ASA	Sine Rule
SSS / SAS	Cosine Rule

6.4

Area of Triangle

Area $= \dfrac{1}{2}ab\sin C$

DSE 2022 Q14

In △ABC, $a = 5$, $b = 7$, $C = 60°$. Find $c$.

$c^2 = 25 + 49 - 70 \times \frac{1}{2} = 39$

$c = \sqrt{39}$

1. If $\sin\theta = \frac{5}{13}$, find $\cos\theta$ and $\tan\theta$ (acute angle).

2. In △ABC, $a = 8$, $A = 30°$, $B = 45°$, find $b$.

3. Find the area of △ABC if $a = 6$, $b = 8$, $C = 30°$.

1. $\cos\theta = \frac{12}{13}$, $\tan\theta = \frac{5}{12}$ 2. $8\sqrt{2}$ 3. $12$

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