note2 - Math021 week 2 Theorem 2.1 For every number x y •...

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Unformatted text preview: Math021, week 2 Theorem 2.1 For every number x , y • sin( x + y ) = sin x cos y + cos x sin y • sin( x- y ) = sin x cos y- cos x sin y • cos( x + y ) = cos x cos y- sin x sin y • cos( x- y ) = cos x cos y + sin x sin y • tan( x + y ) = tan x +tan y 1- tan x tan y • tan( x- y ) = tan x- tan y 1+tan x tan y Corollary 2.2 For every number x , • sin 2 x = 2 sin x cos x • cos 2 x = cos 2 x- sin 2 x = 2 cos 2 x- 1 = 1- 2 sin 2 x • tan 2 x = 2 tan x 1- tan 2 x Theorem 2.3 (cosine law) Let the lengths of the edges of a triangle be a , b , c . Its three angles are A , B , C such that the angle A is opposite to the edge with length a , etc. Then, c 2 = a 2 + b 2- 2 ab cos C. Theorem 2.4 (Sine law) Let the lengths of the edges of a triangle be a , b , c . Its three angles are A , B , C such that the angle A is opposite to the edge with length a , etc. Then, sin A a = sin B b = sin C c . Definition 2.5 Let a > . The function f ( x ) = a x for all x is called the exponential function with base a ....
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This note was uploaded on 02/13/2012 for the course MATH 021 taught by Professor Luxnu during the Fall '10 term at HKUST.

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note2 - Math021 week 2 Theorem 2.1 For every number x y •...

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