RefPages - REFERENCE PAGES Algebra Geometry Arithmetic...

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REFERENCE PAGES Algebra Arithmetic Operations Exponents and Radicals Factoring Special Polynomials Binomial Theorem where Quadratic Formula If , then . Inequalities and Absolute Value If and , then . If , then . If and , then . If and , then . If , then means or means means or Geometry Geometric Formulas Formulas for area A , circumference C , and volume V : Triangle Circle Sector of Circle Sphere Cylinder Cone Distance and Midpoint Formulas Distance between and : Midpoint of : Lines Slope of line through and : Point-slope equation of line through with slope m : Slope-intercept equation of line with slope m and y -intercept b : Circles Equation of the circle with center and radius r : s x 2 h d 2 1 s y 2 k d 2 - r 2 s h , k d y - mx 1 b y 2 y 1 - m s x 2 x 1 d P 1 s x 1 , y 1 d m - y 2 2 y 1 x 2 2 x 1 P 2 s x 2 , y 2 d P 1 s x 1 , y 1 d S x 1 1 x 2 2 , y 1 1 y 2 2 D P 1 P 2 d - s s x 2 2 x 1 d 2 1 s y 2 2 y 1 d 2 P 2 s x 2 , y 2 d P 1 s x 1 , y 1 d h r r h r A - p r s r 2 1 h 2 A - 4 r 2 V - 1 3 r 2 h V - r 2 h V - 4 3 r 3 r r r s ¨ ¨ a h b s - r u s in radians d C - 2 r - 1 2 ab sin A - 1 2 r 2 A - r 2 A - 1 2 bh x , 2 a x . a | x | . a 2 a , x , a | x | , a x - 2 a x - a | x | - a a . 0 ca . cb c , 0 a , b ca , cb c . 0 a , b a 1 c , b 1 c a , b a , c b , c a , b x - 2 b 6 s b 2 2 4 ac 2 a ax 2 1 bx 1 c - 0 S n k D - n s n 2 1 d ??? s n 2 k 1 1 d 1 ? 2 ? 3 ? ? k 1???1 S n k D x n 2 k y k nxy n 2 1 1 y n s x 1 y d n - x n 1 nx n 2 1 y 1 n s n 2 1 d 2 x n 2 2 y 2 s x 2 y d 3 - x 3 2 3 x 2 y 1 3 xy 2 2 y 3 s x 1 y d 3 - x 3 1 3 x 2 y 1 3 2 1 y 3 s x 2 y d 2 - x 2 2 2 1 y 2 s x 1 y d 2 - x 2 1 2 1 y 2 x 3 2 y 3 - s x 2 y ds x 2 1 1 y 2 d x 3 1 y 3 - s x 1 y ds x 2 2 1 y 2 d x 2 2 y 2 - s x 1 y ds x 2 y d n Î x y - s n x s n y s n - s n x s n y x m y n - s n x m - ( s n x ) m x 1 y n - s n x S x y D n - x n y n s d n - x n y n x 2 n - 1 x n s x m d n - x mn x m x n - x m 2 n x m x n - x m 1 n a b c d - a b ± d c - ad bc a 1 c b - a b 1 c b a b 1 c d - ad 1 bc bd a s b 1 c d - ab 1 ac ❙❙❙❙ 1
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❙❙❙❙ 2 Trigonometry Angle Measurement Right Angle Trigonometry Trigonometric Functions Graphs of Trigonometric Functions Trigonometric Functions of Important Angles radians 0010 1 10— p y 2 90 8 s 3 1 y 2 s 3 y 2 y 3 60 8 s 2 y 2 s 2 y 2 y 4 45 8 s 3 y 3 s 3 y 2 1 y 2 y 6 30 8 0 8 tan u cos sin π2 π x y y= cot  x x 1 _1 y π y= sec  x y= csc  x π x y 1 _1 x y π y= tan  x y= cos  x π x y 1 _1 y= sin  x x y 1 _1 π cot - x y tan - y x sec - r x cos - x r (x, y) r ¨ x y csc - r y sin - y r cot - adj opp tan - opp adj sec - hyp adj cos - adj hyp ¨ opp adj hyp csc - hyp opp sin - opp hyp s in radians d s - r 1 rad - 180 8 1 8 - 180 rad r r ¨ s radians - 180 8 Fundamental Identities The Law of Sines The Law of Cosines Addition and Subtraction Formulas Double-Angle Formulas Half-Angle Formulas cos 2 x - 1 1 cos 2 x 2 sin 2 x - 1 2 cos 2 x 2 tan 2 x - 2 tan x 1 2 tan 2 x cos 2 x - cos 2 x 2 sin 2 x - 2 cos 2 x 2 1 - 1 2 2 sin 2 x sin 2 x - 2 sin x cos x tan s x 2 y d - tan x 2 tan y 1 1 tan x tan y tan s x 1 y d - tan x 1 tan y 1 2 tan x tan y cos s x 2 y d - cos x cos y 1 sin x sin y cos s x 1 y d - cos x cos y 2 sin x sin y sin s x 2 y d - sin x cos y 2 cos x sin y sin s x 1 y d - sin x cos y 1 cos x sin y c 2 - a 2 1 b 2 2 2 ab
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This note was uploaded on 02/08/2010 for the course M 340L taught by Professor Lay during the Spring '10 term at École Normale Supérieure.

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RefPages - REFERENCE PAGES Algebra Geometry Arithmetic...

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