Year 2 Flashcards
Double angle formula: sin2A
2sin(A)cos(A)
Double angle formula: cos2A
- ; cos^2(A) - sin^2(A)
- ; 2cos^2(A) - 1
- ; 1 - 2sin^2(A)
Double angle formula: tan2A
2tan(A) / 1-tan^2(A)
Name the two trig identities involving sec^2 and cosec^2:
1 + tan^2(x) = sec^2(x)
1 + cot^2(x) = cosec^2(x)
Name the trig identity involving tan:
Sinx / cosx = tanx
Name the trig identity involving sin^2 and cos^2:
sin^2(x) + cos^2(x) = 1
Differentiate cos(5x):
-5sin(5x)
Differentiate 3sin(5x^2):
30xcos(5x^2)
What is the product rule?
udv/dx + vdu/dx
Differentiate 6lnx:
6 / x
What is the quotient rule?
(v du/dx - u dv/dx) / v^2
Differentiate y = a^kx:
a^kx k lna
Integrate 1/x:
lnx + c
Integrate sin5x:
-1/5 cos5x + c
What is the arithmetic sequence formula?
u = a + (n-1)d
What is the geometric sequence formula?
u = ar^n-1
How to work out arc length?
r x theta
How to work out sector area?
1/2 x r^2 x theta
How to work out segment area?
1/2r^2 x ( theta - sin theta )
What is the general mnemonic to choose u in integration by parts?
Logs
Algebra
Trigonometry
Exponentials
Given a 3D vector how do you calculate the angle between the vector and x,y,z axes?
Cos(theta) = axes(x,y or z) / magnitude of vector
What is the volume of a sphere?
4/3 x pi x r^3