mac1147_review_3 - REVIEW UNIT III MAC1147 FORMULAS TO...

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1 REVIEW UNIT III MAC1147 FORMULAS TO MEMORIZE : Identities: log a x ax = ( 0 x > ), log x a = ( x is any real number) Properties of logarithms ( 0, 0, 0, 1, and 0 xyaa p >>>≠ ): (a) log ( ) log log aa a x yx y =+ (b) log log log a x x y y ⎛⎞ =− ⎜⎟ ⎝⎠ (c) log log r x rx = (d) 1 log log p a a x x p = (e) log 1 a a = (f) log 1 0 a = Change-of-Base Theorem: () log log , , 0 1 1 log b a b x xa b x a b a = >≠ Compound Interest Formula: 1 nt r AP n Continuous Compounding: rt A Pe = Exponential Growth or Decay: ( ) 0 kt A tA e = Length of an Arc ( θ in radians): sr = Area of a Sector ( in radians): 2 1 2 A r = Linear Speed: s t υ = Angular Speed: t ω = Relation between and : r = ( in radians) Trigonometric Identities: sin tan cos = cos cot sin = tan cot 1 ⋅= 1 csc sin = 1 sec cos = 1 tan cot = 22 sin cos 1 θθ += tan 1 sec 1c o t c s c sin 2 sin n πθ ( ) cos 2 cos n tan tan n sin sin ±= ( ) cos cos cos cos −= ( ) sin sin tan tan Sum and Difference Formulas: ( ) cos cos cos sin sin α βα β ( ) cos cos cos sin sin + ( ) sin sin cos cos sin + ( ) sin sin cos cos sin
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2 () tan tan tan 1t a nt a n α β αβ + += tan tan tan a a n −= + Double-angle Formulas: 22 cos2 cos sin θ θθ =− 2 2cos 1 = 2 1 2sin sin 2 2sin cos = 2 2tan tan2 a n = Half-angle Formulas: 1c o s sin o s cos + o s tan 21 c o s + sin tan 21c o s = + o s tan 2s i n = General Formulas for the Solutions of the Trigonometric Equations: ( 0, 1, 2,. .. k =±± ) sin a = ( 1 a ) arcsin 2 ak π =+ and ( arcsin ) 2 ππ = −+ cos a = ( 1 a ) arccos 2 and (2 arccos ) 2 = O R arccos 2 + tan a = arctan The Law of Sines: sin sin sin abc βγ == The Law of Cosines: 222 2c o s cab a b γ =+− Area of a Triangle: 1 2 A bh = 1 sin 2 Aa b = ( )( ) As s a s b s c (Heron’s Formula), 1 2 s + The Binomial Formula: 0 n n nj j j n x yx y j = ⎛⎞ ⎜⎟ ⎝⎠ , where !
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This note was uploaded on 11/07/2011 for the course MAC 1147 taught by Professor German during the Summer '08 term at University of Florida.

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mac1147_review_3 - REVIEW UNIT III MAC1147 FORMULAS TO...

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