# Trigonometry

### Definitions:

$sinθ = opposite hypotenuse$
$cosθ = adjacent hypotenuse$
$tanθ = opposite adjacent$

## Trig Values to Remember

Angledegrees / °030456090
radians 0 $\frac{\pi }{6}$ $\frac{\pi }{4}$$\frac{\pi }{3}$$\frac{\pi }{2}$
sine0$\frac{1}{2}$$\frac{\sqrt{2}}{2}$$\frac{\sqrt{3}}{2}$1
cosine1$\frac{\sqrt{3}}{2}$$\frac{\sqrt{2}}{2}$$\frac{1}{2}$0
tangent0$\frac{\sqrt{3}}{3}$1$\sqrt{3}$[undefined]

### The Law of Sines(AKA the sine rule)

$sinAa=sinBb=sinCc$

### al-Kashi's Theorem(AKA the cosine rule)

$c2 = a2 + b2 - 2⁢a⁢b⁢cosC$

### Trigonometric Identities

$tanx=sinxcosx$ $cosecx=1sinx$ $secx=1cosx$ $cotx=1tanx$ $sin2θ+cos2θ=1$ $1+cot2θ=cosec2θ$ $tan2θ+1=sec2θ$
$sin(A±B) = sinA⁢cosB± sinB⁢cosA$ $sin2⁢A = 2⁢sinA⁢cosA$ $cos(A±B) = cosA⁢cosB∓ sinB⁢sinA$ $cos2⁢A = cos2A-sin2A$ $= 2⁢cos2A-1$ $= 1-2⁢sin2A$ $tan(A±B) = tanA±tanB 1∓tanA⁢tanB$ $tan2⁢A = 2⁢tanA 1-tan2A$

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