Stuff to Memorise Flashcards
sin rules
-sin(θ) = sin(-θ)
cos(θ) = cos(-θ)]
cos(θ) = cos(360 - θ)
sin(θ) = sin(180 - θ)
Argand Diagram Axes
X: Real Part
Y: Imaginary Part
Argument
The angle the positive real axis and the line joining z to the origin
Quadrant:
1: arg(z) = x
2: arg(z) = pi - x
3: arg(z) = -(pi-x)
4: arg(z) = -x
x is the angle made between the line joining z and the origin and the real axis
Sum of Squares
(Sum of the roots)^2 - 2(Sum of the pairs)
Sum of Cubes
(Sum of the roots)^3 -3(Sum of the roots)(Sum of the pairs)
If cubic: + 3(product of the roots)
Two way stretch in the x-direction scale factor a
y-direction scale factor b
a 0
0 b
Enlargement Scale Factor K centre the origin
k 0
0 k
Rotation through the angle θ anticlockwise about the origin
cos θ -sin θ
sin θ cos θ
Reflection in the Y-Axis
-1 0
0 1
Reflection in the X-Axis
1 0
0 -1
Reflection in the line y = x
0 1
1 0
Reflection in the line y = -x
0 -1
-1 0
Determinant of matrix:
a b
c d
ad - bc
Reflection in the plane x = 0
-1 0 0
0 1 0
0 0 1
Reflection in the plane y = 0
1 0 0
0 -1 0
0 0 1
Reflection in the plane z = 0
1 0 0
0 1 0
0 0 -1
Rotation Angle θ about the x-axis
1 0 0
0 cosθ -sinθ
0 sinθ cosθ
Rotation Angle θ about the y-axis
cosθ 0 sinθ
0 1 0
-sinθ 0 cosθ
Rotation Angle θ about the z-axis
cosθ -sinθ 0
sinθ cosθ 0
0 0 1
Consistent Equations
At least one set of values which satisfies all three of the equations
Inconsistent Equations
No set of values satisfy all three equations
Inverse of matrix
a b
c d
1/det x d -b
-c a
