C4 Flashcards
sin2A = ?
2sinAcosA
cos2A = ?
cos²A - sin²A
2cos²A - 1
1 - 2sin²A
tan2A = ?
2tanA/(1 - tan²A)
sin4x = ?
2sin2xcos2x
d/dx sinax = ?
acosax
d/dx cosax = ?
-asinax
d/dx sinx = ?
cosx
d/dx cosx = ?
-sinx
d/dx sin(ax + b) = ?
acos(ax+b)
d/dx cos(ax + b) = ?
-asin(ax +b)
How would you differentiate sin²x?
Chain rule of (sinx)²
to obtain 2⋅(d/dx sinx)⋅(sinx)²⁻¹
= 2⋅cosx⋅sinx
= sin2x
How would you differentiate cos²x?
Chain rule of (cosx)² to obtain 2⋅(d/dx cosx)⋅(cosx)²⁻¹ = 2⋅-sinx⋅cosx = -2sinxcosx = - sin2x
How do you make parametric equations cartesian?
Eliminate the parameter
dy/dx of a parametric equation?
dy/dx = dy/dt ⋅ dt/dx = g’(t)/f’(t)
Implicit: d/dx y = ?
dy/dx
Implicit: d/dx y² = ?
2y⋅dy/dx
Implicit: d/dx xy = ?
u = x, v = y u' = 1, v' =dy/dx
∴ d/dx xy = vu’ + uv’
∴ d/dx xy = x⋅dy.dx + y
∫ sinax dx = ?
-1/a cosax + c
∫ cosax dx = ?
1/a sinax + c
∫ sec²ax dx = ?
1/a tanax + c
∫ kf’(x)/f(x) dx = ?
kln|f(x)| + c
Formula for Integration by parts?
∫ uv’ dx = uv - ∫ vu’ dx
where u is a value that will differentiate to a constant, or is lnx
Steps for Integration by substitution?
|> u = f(x)
|> Make obvious substitution (change f(x) for u)
|> Differentiate u = f(x) and rearrange for dx
|> Rearrange u = f(x) for x=
|> Integrate with respect to u
|> Change limits
|> Replace u with f(x)
a/b ⋅ c/d = ?
ac/bd