- Created by: Georgia
- Created 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)
What are the trig identities involving Cot^2(x) an
1 + Cot^2(x) = Cosec^2(x)
What are the trig identities involving Tan^2(x) an
Tan^2(x) + 1 = Sec^2(x)
What is the trig identity for Sin(2x)?
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
What is the trig identity for Tan(2x)?
2Tan(x) / 1 - Tan^2(x)
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.
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
Differentiation and Integration
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
Raise power by one, divide by new power * differential of the bracket
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)