Maths - Core 3 3.0 / 5 MathematicsA2/A-levelOCR Created by: GeorgiaCreated on: 14-04-13 15:23 What are the trig identities involving sin^2(x) an Sin^2(x) + Cos^2(x) = 1 Sin^2(x) = 1 - Cos^2(x) Cos^2(x) = 1 - Sin^2(x) 1 of 10 What are the trig identities involving Cot^2(x) an 1 + Cot^2(x) = Cosec^2(x) 2 of 10 What are the trig identities involving Tan^2(x) an Tan^2(x) + 1 = Sec^2(x) 3 of 10 What is the trig identity for Sin(2x)? 2Sin(x)Cos(x) 4 of 10 What are the three trig identities for Cos(2x)? Cos(2x) = Cos^2(x) - Sin^2(x) Cos(2x) = 1 - 2Sin^2(x) Cos(2x) = 2Cos^2(x) - 1 5 of 10 What is the trig identity for Tan(2x)? 2Tan(x) / 1 - Tan^2(x) 6 of 10 Exponentials In(1) = 0 In(e) = 1 In(e^x) = x e^(Inx) = x For y = Ae^kx, k>0 = Growth, k<0 = Decay. For f(t) = A x b^t, b>1 = Growth, 0<b<1 = Decay. 7 of 10 Calculus y = Ae^kx+b, Differential = (Ak)e^kc+b y = Ae^kx+b, Integral = Ae^kx+b / k y = In(f(x)), Differential = f '(x) / f(x) y = 1/x, Integral = In|x| Discriminants - for quadratics; (Can relate to stationary points) <0 NO SOLUTIONS =0 ONE REPEATED SOLUTION >0 TWO DISTINCT SOLUTIONS 8 of 10 Differentiation and Integration Differentiation; Bracket Rule - Times number outside by power, lower power, multiply by differential Chain Rule - Let u = ....... Product Rule - u'v + uv' Quotient Rule - (u'v - uv') / v^2 Integration; Raise power by one, divide by new power * differential of the bracket 9 of 10 Volume of Revolution 360' Rotation about x-axis, V = pi * definite integral of y^2 360' Rotation about y-axis, V = pi * definite intergral of x^2 (Rearrange y = ..so x is subject) 10 of 10

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