All Flashcards

1
Q

sin(A ± B) =

A

sinAcosB ± cosAsinB

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2
Q

cos(A ± B) =

A

cosAcosB ∓ sinAsinB

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3
Q

sin2A =

A

2sinAcosA

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4
Q

cos2A =

A

cos(squared)A - sin(squared)A

or

2cos(squared)A - 1

or

1 - 2sin(squared)A

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5
Q

sin(squared)A + cos (squared)A =

A

1

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6
Q

sinA / cosA =

A

tanA

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7
Q

Partial Fractions: distinct linear factors

ax + b / (cx + d)(ex + f) =

A

A / (cx + d) + B / (ex + f)

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8
Q

Partial Fractions: repeated linear factor

ax(squared) + bx + c /(dx + e) (fx +g)(squared)

A

A / (dx + e) + B / (fx + g) + C / (fx + g)(squared)

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9
Q

Partial Fractions: irreducible quadratic

ax(squared) + bx + c / (dx + e)(fx(squared) + gx + h)

A

A / (dx + e) + Bx + C / (fx(squared) + gx + h)

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10
Q

Calculus is always done in degrees or radians?

A

Radians

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11
Q

Product Rule:

k(x) = f(x) . g(x)

k’(x) =

A

f’(x) . g(x) + f(x) . g’(x)

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12
Q

Quotient Rule:

k(x) = f(x) / g(x)

k’(x) =

A

f’(x) . g(x) - f(x) . g’(x) / (g(x))(squared)

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13
Q

1 / cos(x) =

A

sec(x)

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14
Q

1 / sin(x) =

A

cosec(x)

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15
Q

1 / tan(x) = cos(x) / sin(x) =

A

cot(x)

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16
Q

tan(squared)x =

A

sec(squared)x - 1

17
Q

f’‘(x) > 0, curve lies…

f’‘(x) < 0, curve lies…

A

…above tangent, gradient increasing.

…below tangent, gradient decreasing.

18
Q

Implicit differentiation:

A

Same as normal differentiation, where d (y) / dx = dy/dx

19
Q

Second derivative of implicit functions are easier to find if you…

A

…differentiate dy/dx again before simplifying.

20
Q

Parametric Differentiation:

dy/dx =

d(squared)y/dx(squared) =

A

dy/dt / dx/dt

d(dy/dx) / dt . 1 / dx/dt - Differentiate first derivative with respect to t then divide by dx/dt.