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 a x = ( 0 x > ), log x a a x = ( x is any real number) Properties of logarithms ( 0, 0, 0, 1, and 0 x y a a p > > > ): (a) log ( ) log log a a a xy x y = + (b) log log log a a a x x y y = (c) log log r a a x r x = (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 x a b x a b a = > Compound Interest Formula: 1 nt r A P n = + Continuous Compounding: rt A Pe = Exponential Growth or Decay: ( ) 0 kt A t A e = Length of an Arc ( θ in radians): s r θ = Area of a Sector ( θ in radians): 2 1 2 A r θ = Linear Speed: s t υ = Angular Speed: t θ ω = Relation between υ and ω : r υ ω = ( θ in radians) Trigonometric Identities: sin tan cos θ θ θ = cos cot sin θ θ θ = tan cot 1 θ θ = 1 csc sin θ θ = 1 sec cos θ θ = 1 tan cot θ θ = 2 2 sin cos 1 θ θ + = 2 2 tan 1 sec θ θ + = 2 2 1 cot csc θ θ + = ( ) sin 2 sin n θ π θ + = ( ) cos 2 cos n θ π θ + = ( ) tan tan n θ π θ + = ( ) sin sin θ π θ ± = − ( ) cos cos θ π θ ± = − ( ) cos cos θ θ = ( ) sin sin θ θ = − ( ) tan tan θ θ = − Sum and Difference Formulas: ( ) cos cos cos sin sin α β α β α β + = ( ) cos cos cos sin sin α β α β α β = + ( ) sin sin cos cos sin α β α β α β + = + ( ) sin sin cos cos sin α β α β α β =
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