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161-f11-sg1-09-08

161-f11-sg1-09-08 - Fall 2011 MA 16100 Study Guide Exam 1(1...

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Unformatted text preview: Fall 2011 MA 16100 Study Guide - Exam # 1 (1) Review of Algebra : (a) Equalities, inequalities, absolute values (b) Distance between P ( x 1 ,y 1 ) and P ( x 2 ,y 2 ) is | PQ | = radicalBig ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 . (c) Equations of lines: (i) Point-Slope Form : y − y 1 = m ( x − x 1 ) (ii) Slope-Intercept Form : y = mx + b (d) L 1 || L 2 ⇐⇒ m 1 = m 2 ; L 1 ⊥ L 2 ⇐⇒ m 2 = − 1 m 1 (e) Equation of a circle: ( x − h ) 2 + ( y − k ) 2 = r 2 . (2) Review of Trigonometry : (a) Length of arc subtended by θ : a = rθ a r θ (b) Definition of trig functions (cos θ, sin θ, tan θ, csc θ, sec θ, cot θ ); basic trig values of well- know angles. r y x θ 1-1-1 (cos ,sin ) θ θ 1 x y θ (c) Basic trig identities (including): (i) braceleftBigg sin 2 θ + cos 2 θ = 1 tan 2 θ + 1 = sec 2 θ (ii) braceleftBigg sin( − θ ) = − sin θ cos( − θ ) = cos θ (iii) braceleftBigg sin( θ + 2 π ) = sin θ cos( θ + 2 π ) = cos θ (iv) braceleftBigg sin 2 θ = 2 sin θ cos θ cos 2 θ = cos 2 θ − sin 2 θ (v) sin 2 θ = 1 − cos 2 θ 2 cos 2 θ = 1 + cos 2 θ 2 1 (3) Functions (a) Functions; Vertical Line Test ; domain and range of a function; piecewise defined...
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161-f11-sg1-09-08 - Fall 2011 MA 16100 Study Guide Exam 1(1...

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