Trigonometry and Solid Measurements Flashcards
1
Q
Trigonometric Functions
csc A =
A
1/sin A
2
Q
Trigonometric Functions
tan A =
A
sin A/cos A
3
Q
Trigonometric Functions
sec A =
A
1/cos A
4
Q
Trigonometric Functions
cot A =
A
1/tanA
5
Q
Pythagorean Relations
A
6
Q
Functions of Complementary Angles:
cos A =
cot A =
csc A =
A
7
Q
Sum and Difference of Angles:
A
8
Q
Sum and Difference of Angles
A
9
Q
Sum and Difference of Angles
A
10
Q
sin 2A =
A
2sinAcosA
11
Q
cos 2A =
A
12
Q
tan 2A
A
13
Q
A
14
Q
A
15
Q
A
16
Q
Sine Law (ASA)
A
17
Q
Cosine Law (SSS, SAS)
A
18
Q
Area of Right Triangle
A
A= ab/2
19
Q
Area of triangle given SSS
A
20
Q
Area of triangle given SAS
A
21
Q
Area of Triangle inscribed in a circle
A
22
Q
Area of Triangle circumscribed a circle
A
A = rs
23
Q
Area of triangle with escribed circle
A
24
Q
Length of median of a triangle
A
25
Degrees to mil conversion
360 deg = 6400 mil
26
area of a triangle circumscribed by circle shortcut:
sine law = 2r
27
Area of circle
28
Circumference of Circle
29
Arc length of a circle
30
Area of a sector of circle
31
Area of a segment in a circle
32
4 sides equal, 4 right angles, diagonals are perpendicular
square
33
Area of a square
34
Perimeter of a square
P = 4s
35
Opposite sides are equal, 4 right angles
Rectangle
36
Area of a rectangle
A = LW
37
Perimeter of rectangle
P = 2L + 2W
38
4 sides may be equal, diagonals are perpendicular
Rhombus
39
Area of Rhombus
40
Perimeter of a rhombus
P = 4s
41
Opposite sides are equal and parallel
Parallelogram
42
Area of a parallelogram
43
Perimeter of a parallelogram
P = 2(S1 +S2)
44
two pairs of adjacent sides equal, diagonals are perpendicular
Kite
45
Area of a Kite
46
Perimeter of kite
P =2(S1 +S2)
47
two sides are parallel only
trapezoid
48
Area of a trapezoid
49
with 4 sides not equal and not parallel with two diagonals and intersection are known
Quadrilateral
50
Area of Quadrilateral
51
Quadrilateral inscribed in a circle
Cyclic quadrilateral
52
Area of circle with ciclic quadrilateral
53
Radius of a circle with cyclic quadrilateral
54
Ptolemy theorem in cyclic quadrilateral
55
Area of a circle inscribed in a quadrilateral (cyclic quadrilateral circumscribed a circle)
56
Radius of a circle inscribed in a quadrilateral (Cyclic Quadrilateral)
57
POLYGON
Sum of interior angle
58
POLYGON
Size of interior angle
59
POLYGON
Sum of exterior angle
S = 360 degrees
60
POLYGON
Size of exterior angle
61
POLYGON
Number of Diagonals
62
Area of a regular polygon
63
Perimeter of a regular polygon
P=n(side)
64
area of quadrilateral approximation
65
a line from the center of a regular polygon at right angles to any of its sides
Apothem
66
Name the common regular polygons from 3 to 20 sides
67
name common regular polygons from 20 to 100 with increments of 10 (20, 30, 40, ..., 100)
68
Cube
Volume:
Surface Area:
Space Diagonal:
69
Rectangular Parallelepiped
Volume:
Surface Area:
Space Diagonal:
70
Right Cylinder
Volume:
Surface Area:
Lateral Area:
71
Right Cone
Volume:
Surface Area:
Lateral Area:
72
Right Pyramid
Volume:
Surface Area:
Lateral Area:
73
(shortcut) Percent increase from single dimension to square dimension:
74
(shortcut) Percent increase from square dimension to single dimension:
75
(shortcut) Percent increase from single dimension to cube dimension:
76
(shortcut) Percent increase from double dimension to cube dimension:
77
Right Frustrum
Volume:
Surface Area:
Lateral Area:
78
Sphere
Volume:
Surface Area:
79
Formula for zone
80
Spherical Segment (1 base)
Volume:
Surface Area:
81
Spherical Sector/Spherical Cone
Volume:
82
Spherical Wedge
Volume:
83
Spherical lune surface area
84
polyhedron four equal faces of equilateral triangle
tetrahedron
85
Tetrahedron
# of faces:
# of vertices:
# of edges:
Euler's Equation:
86
Tetrahedron
Total Surface Area:
Volume:
Radius of inscribed sphere:
87
six square equal faces polyhedron
hexahedron
88
Hexahedron
# of faces:
# of vertices:
# of edges:
Euler's Equation:
f = 6
v = 8
e = 12
f + v - e = 2
89
Hexahedron
Total surface area:
Volume:
Radius of inscribed sphere:
90
Eight equilateral triangle faces polyhedron
octahedron
91
Octahedron:
# of faces:
# of vertices:
# of edges:
Euler's Equation:
f = 8
v = 6
e = 12
f + v - e = 2
92
Octahedron
Total Surface Area:
Volume:
Radius of Inscribed Sphere:
93
Dodecahedron
No. of faces:
No. of vertices:
No. of edges:
Euler's Equation
94
12 equal pentagon faces of polyhedron
Dodecahedron
95
Dodecahedron
Total Surface Area:
Volume:
Radius of inscribed sphere:
96
twenty quadrilateral triangle faces of polyhedron
Icosahedron
97
Icosahedron
No. of faces:
No. of vertices:
No of edges:
Euler's Equation:
98
Icosahedron
Total Surface Area:
Volume:
Radius of inscribed sphere:
