Trigonometric functions – Singapore Maths Tuition

A Maths Tuition: Trigonometry Formulas

Many students find Trigonometry in A Maths challenging.

This is a list of Trigonometry Formulas that I compiled for A Maths. Students in my A Maths tuition class will get a copy of this, neatly formatted into one A4 size page for easy viewing.

A Maths: Trigonometry Formulas

$\mathit{cosec}x=\frac{1}{\sin x}$ ; $\mathit{sec}x=\frac{1}{\cos x}$

$\cot x=\frac{1}{\tan x}$ ; $\tan x=\frac{\sin x}{\cos x}$

(All Science Teachers Crazy)

$y=\sin x$

$y=\cos x$

$y=\tan x$

$\frac{d}{\mathit{dx}}(\sin x)=\cos x$

$\frac{d}{\mathit{dx}}(\cos x)=-\sin x$

$\frac{d}{\mathit{dx}}(\tan x)=\mathit{sec}^{2}x$

$\int {\sin x\mathit{dx}}=-\cos x+c$

$\int \cos x\mathit{dx}=\sin x+c$

$\int \mathit{sec}^{2}x\mathit{dx}=\tan x+c$

Special Angles:

$\cos 45^\circ=\frac{1}{\sqrt{2}}$

$\cos 60^\circ=\frac{1}{2}$

$\cos 30^\circ=\frac{\sqrt{3}}{2}$

$\sin 45^\circ=\frac{1}{\sqrt{2}}$

$\sin 60^\circ=\frac{\sqrt{3}}{2}$

$\sin 30^\circ=\frac{1}{2}$

$\tan 45^\circ=1$

$\tan 60^\circ=\sqrt{3}$

$\tan 30^\circ=\frac{1}{\sqrt{3}}$

$y=a\sin (\mathit{bx})+c$ Amplitude: $a$ ; Period: $\frac{2\pi }{b}$

$y=a\cos (\mathit{bx})+c$ Amplitude: $a$ ; Period: $\frac{2\pi }{b}$

$y=a\tan (\mathit{bx})+c$ Period: $\frac{\pi }{b}$

$\pi \mathit{rad}=180^\circ$

Area of $\triangle \mathit{ABC}=\frac{1}{2}\mathit{ab}\sin C$

Sine Rule: $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

Cosine Rule: $c^{2}=a^{2}+b^{2}-2\mathit{ab}\cos C$