All the stuff Flashcards
1 + tan²ϴ =
sec²ϴ
1 + cot²ϴ =
cosec²ϴ
Sin2ϴ
2sinϴcosϴ
Cos2ϴ (to cos and sin)
Cos²ϴ - Sin²ϴ
Cos2ϴ(to cos)
2Cos²ϴ - 1
Cos2ϴ(to sin)
1 - 2Sin²ϴ
Tan2ϴ
2Tanϴ / 1 - Tan²ϴ
secϴ
1/cosϴ
cosecϴ
1/sinϴ
cotϴ
1/tanϴ = cosϴ/sinϴ
Equation of line passing through (a1,a2,a3) in direction (u1,u2,u2) in vector form
r = (a1)………..(u1)
……(a2)+…..λ(u2)
……(a3)……….(u3)
Equation of line passing through (a1,a2,a3) in direction (u1,u2,u2) Cartesian form
(x-a1)/u1 = (y-a2)/u2 = (z-a3)/u3
angle between two vectors is given by
Cosθ = a.b / |a|.|b| |a| = sum of the xyz components squared and square rooted
the Cartesian equation for a plane perpendicular to (n1) ……………………………………………………………………………………..(n2)
……………………………………………………………………………………..(n3)
(n1)X + (n2)Y + (n3)Z + d = 0
the vector perpendicular to the plane (n1)X + (n2)Y + (n3)Z + d = 0
(n1)
(n2)
(n3)
Distance of a point from a plane is found by
construct a line perpendicular to the plane and through the given point , find where the line intersects the plane, find the distance between the two points
2 / (x+1)(x+2) in partial fractions
a/(x+1) + b/(x+2)
2x + 1 / (x²+1)(x+2) in partial fractions
ax+b/(x²+1) + c/(x+2)
2x + 1 / (x+1)²(x+2) in partial fractions
a/(x+1) + b/(x²+1) + c/(x+2)
integrating partial fraction e.g 2 / (x+1)(x+2)
∫a/(x+1) + ∫b/(x+2)
Differentiating parametric equation
(dy/dt) / (dx/dt)
Volume rotated 360 about x axis
V = π ∫y² dx
Volume rotated 360 about y axis
V = π ∫x² dy
e.g dy/dx = 2x becomes
y = x² + c
e to the power of a constant is given as
A
