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M > Trigonometry and Solid Measurements > Flashcards

Trigonometry and Solid Measurements Flashcards

1
Q

Trigonometric Functions

csc A =

A

1/sin A

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2
Q

Trigonometric Functions
tan A =

A

sin A/cos A

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3
Q

Trigonometric Functions
sec A =

A

1/cos A

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4
Q

Trigonometric Functions
cot A =

A

1/tanA

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5
Q

Pythagorean Relations

A
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6
Q

Functions of Complementary Angles:
cos A =
cot A =
csc A =

A
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7
Q

Sum and Difference of Angles:

A
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8
Q

Sum and Difference of Angles

A
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9
Q

Sum and Difference of Angles

A
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10
Q

sin 2A =

A

2sinAcosA

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11
Q

cos 2A =

A
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12
Q

tan 2A

A
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13
Q
A
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14
Q
A
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15
Q
A
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16
Q

Sine Law (ASA)

A
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17
Q

Cosine Law (SSS, SAS)

A
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18
Q

Area of Right Triangle

A

A= ab/2

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19
Q

Area of triangle given SSS

A
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20
Q

Area of triangle given SAS

A
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21
Q

Area of Triangle inscribed in a circle

A
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22
Q

Area of Triangle circumscribed a circle

A

A = rs

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23
Q

Area of triangle with escribed circle

A
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24
Q

Length of median of a triangle

A
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25
Q

Degrees to mil conversion

A

360 deg = 6400 mil

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26
Q

area of a triangle circumscribed by circle shortcut:

A

sine law = 2r

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27
Q

Area of circle

A
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28
Q

Circumference of Circle

A
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29
Q

Arc length of a circle

A
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30
Q

Area of a sector of circle

A
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31
Q

Area of a segment in a circle

A
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32
Q

4 sides equal, 4 right angles, diagonals are perpendicular

A

square

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33
Q

Area of a square

A
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34
Q

Perimeter of a square

A

P = 4s

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35
Q

Opposite sides are equal, 4 right angles

A

Rectangle

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36
Q

Area of a rectangle

A

A = LW

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37
Q

Perimeter of rectangle

A

P = 2L + 2W

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38
Q

4 sides may be equal, diagonals are perpendicular

A

Rhombus

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39
Q

Area of Rhombus

A
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40
Q

Perimeter of a rhombus

A

P = 4s

41
Q

Opposite sides are equal and parallel

A

Parallelogram

42
Q

Area of a parallelogram

A
43
Q

Perimeter of a parallelogram

A

P = 2(S1 +S2)

44
Q

two pairs of adjacent sides equal, diagonals are perpendicular

A

Kite

45
Q

Area of a Kite

A
46
Q

Perimeter of kite

A

P =2(S1 +S2)

47
Q

two sides are parallel only

A

trapezoid

48
Q

Area of a trapezoid

A
49
Q

with 4 sides not equal and not parallel with two diagonals and intersection are known

A

Quadrilateral

50
Q

Area of Quadrilateral

A
51
Q

Quadrilateral inscribed in a circle

A

Cyclic quadrilateral

52
Q

Area of circle with ciclic quadrilateral

A
53
Q

Radius of a circle with cyclic quadrilateral

A
54
Q

Ptolemy theorem in cyclic quadrilateral

A
55
Q

Area of a circle inscribed in a quadrilateral (cyclic quadrilateral circumscribed a circle)

A
56
Q

Radius of a circle inscribed in a quadrilateral (Cyclic Quadrilateral)

A
57
Q

POLYGON
Sum of interior angle

A
58
Q

POLYGON
Size of interior angle

A
59
Q

POLYGON
Sum of exterior angle

A

S = 360 degrees

60
Q

POLYGON
Size of exterior angle

A
61
Q

POLYGON
Number of Diagonals

A
62
Q

Area of a regular polygon

A
63
Q

Perimeter of a regular polygon

A

P=n(side)

64
Q

area of quadrilateral approximation

A
65
Q

a line from the center of a regular polygon at right angles to any of its sides

A

Apothem

66
Q

Name the common regular polygons from 3 to 20 sides

A
67
Q

name common regular polygons from 20 to 100 with increments of 10 (20, 30, 40, …, 100)

A
68
Q

Cube
Volume:
Surface Area:
Space Diagonal:

A
69
Q

Rectangular Parallelepiped
Volume:
Surface Area:
Space Diagonal:

A
70
Q

Right Cylinder
Volume:
Surface Area:
Lateral Area:

A
71
Q

Right Cone
Volume:
Surface Area:
Lateral Area:

A
72
Q

Right Pyramid
Volume:
Surface Area:
Lateral Area:

A
73
Q

(shortcut) Percent increase from single dimension to square dimension:

A
74
Q

(shortcut) Percent increase from square dimension to single dimension:

A
75
Q

(shortcut) Percent increase from single dimension to cube dimension:

A
76
Q

(shortcut) Percent increase from double dimension to cube dimension:

A
77
Q

Right Frustrum
Volume:
Surface Area:
Lateral Area:

A
78
Q

Sphere
Volume:
Surface Area:

A
79
Q

Formula for zone

A
80
Q

Spherical Segment (1 base)
Volume:
Surface Area:

A
81
Q

Spherical Sector/Spherical Cone
Volume:

A
82
Q

Spherical Wedge
Volume:

A
83
Q

Spherical lune surface area

A
84
Q

polyhedron four equal faces of equilateral triangle

A

tetrahedron

85
Q

Tetrahedron
# of faces:
# of vertices:
# of edges:
Euler’s Equation:

A
86
Q

Tetrahedron
Total Surface Area:
Volume:
Radius of inscribed sphere:

A
87
Q

six square equal faces polyhedron

A

hexahedron

88
Q

Hexahedron
# of faces:
# of vertices:
# of edges:
Euler’s Equation:

A

f = 6
v = 8
e = 12
f + v - e = 2

89
Q

Hexahedron
Total surface area:
Volume:
Radius of inscribed sphere:

A
90
Q

Eight equilateral triangle faces polyhedron

A

octahedron

91
Q

Octahedron:
# of faces:
# of vertices:
# of edges:
Euler’s Equation:

A

f = 8
v = 6
e = 12
f + v - e = 2

92
Q

Octahedron
Total Surface Area:
Volume:
Radius of Inscribed Sphere:

A
93
Q

Dodecahedron
No. of faces:
No. of vertices:
No. of edges:
Euler’s Equation

A
94
Q

12 equal pentagon faces of polyhedron

A

Dodecahedron

95
Q

Dodecahedron
Total Surface Area:
Volume:
Radius of inscribed sphere:

A
96
Q

twenty quadrilateral triangle faces of polyhedron

A

Icosahedron

97
Q

Icosahedron
No. of faces:
No. of vertices:
No of edges:
Euler’s Equation:

A
98
Q

Icosahedron
Total Surface Area:
Volume:
Radius of inscribed sphere:

A

M (12 decks)

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