Formula Booklet

Part if Topic	Name	Equation
3.1	Length of arc	$l = θ r$
3.1	Area of sector	$A = \frac{1}{2} θ r^{2}$
3.2	Trigonometric identity	$\tan θ = \frac{\sin θ}{\cos θ}$
3.3	Pythagorean identity	$\cos^{2} θ + \sin^{2} θ = 1$
3.3	Double angle formulae	$\sin 2 θ = 2 \sin θ \cos θ \cos 2 θ = \cos^{2} θ - \sin^{2} θ = 2 \cos^{2} θ - 1 = 1 - \sin^{2} θ$
3.6	Cosine rule	$c^{2} = a^{2} + b^{2} - 2 a b \cos C \cos C = \frac{a^{2} + b^{2} + c^{2}}{2 a b}$
	Sine rule	$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$
	Area of triangle	$A = \frac{1}{2} a b \sin C$

Basics and Main rules

Triangles
	Soh Cah Toa =	$s in θ = \frac{o p p o s i t e}{h y p o t e n u s e} = \frac{a}{c}$
		$c os θ = \frac{a d j a c e n t}{h y p o t e n u s e} = \frac{b}{c}$
		$t an θ = \frac{o p p o s i t e}{a d j a c e n t} = \frac{a}{b}$

Find side a:

Question	Solution
Find side a, when $L$ A is 62° and side b is 8	$\tan θ = \frac{o p p o s i t e}{a d j a c e n t}$ $\tan (62) = \frac{a}{8}$ $a = \tan (62) \times 8$ $a = 15.05$	Identify the appropriate equation Input the values Rearrange Calculate

\frac{a}{s i n A} = \frac{b}{s i n B} = \frac{c}{s i n C}

\frac{s i n A}{a} = \frac{s i n B}{b} = \frac{s i n C}{c}

Used when you know 3 out of these values - $\frac{a}{\sin A} = \frac{b}{\sin B}$

Question	Solution
Find $L$ B, when side a is 2 and c is 3	$\frac{\sin A}{a} = \frac{\sin B}{b}$ $\frac{\sin (28.9)}{3} = \frac{\sin B}{4}$ $B = \sin^{- 1} (4 \times \frac{\sin (28.9)}{3})$ $B = 40.12$	Identify the appropriate equation Input the values Rearrange Calculate

c^{2} = a^{2} + b^{2} - 2 a b \cos C

\cos C = \frac{a^{2} + b^{2} - c^{2}}{2 a b}

Used when you know 3 out of these values - $c^{2} = a^{2} + b^{2} - 2 a b c o s C$

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Question	Solution
Find side c, when $L$ C is 46.6, side a is 2 and side b is 4	$c^{2} = a^{2} + b^{2} - 2 a b \cos C$ $c^{2} = 2^{2} + 4^{2} - 2 \times 2 \times 4 \times \cos (46.6)$ $c = \sqrt{2^{2} + 4^{2} - 2 \times 2 \times 4 \times \cos (46.6)}$ $c = 3.00$	Identify the appropriate equation Input the values Rearrange Calculate

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