Trigonometry and Solid Measurements Flashcards
Trigonometric Functions
csc A =
1/sin A
Trigonometric Functions
tan A =
sin A/cos A
Trigonometric Functions
sec A =
1/cos A
Trigonometric Functions
cot A =
1/tanA
Pythagorean Relations
Functions of Complementary Angles:
cos A =
cot A =
csc A =
Sum and Difference of Angles:
Sum and Difference of Angles
Sum and Difference of Angles
sin 2A =
2sinAcosA
cos 2A =
tan 2A
Sine Law (ASA)
Cosine Law (SSS, SAS)
Area of Right Triangle
A= ab/2
Area of triangle given SSS
Area of triangle given SAS
Area of Triangle inscribed in a circle
Area of Triangle circumscribed a circle
A = rs
Area of triangle with escribed circle
Length of median of a triangle
Degrees to mil conversion
360 deg = 6400 mil
area of a triangle circumscribed by circle shortcut:
sine law = 2r
Area of circle
Circumference of Circle
Arc length of a circle
Area of a sector of circle
Area of a segment in a circle
4 sides equal, 4 right angles, diagonals are perpendicular
square
Area of a square
Perimeter of a square
P = 4s
Opposite sides are equal, 4 right angles
Rectangle
Area of a rectangle
A = LW
Perimeter of rectangle
P = 2L + 2W
4 sides may be equal, diagonals are perpendicular
Rhombus
Area of Rhombus
Perimeter of a rhombus
P = 4s
Opposite sides are equal and parallel
Parallelogram
Area of a parallelogram
Perimeter of a parallelogram
P = 2(S1 +S2)
two pairs of adjacent sides equal, diagonals are perpendicular
Kite
Area of a Kite
Perimeter of kite
P =2(S1 +S2)
two sides are parallel only
trapezoid
Area of a trapezoid
with 4 sides not equal and not parallel with two diagonals and intersection are known
Quadrilateral
Area of Quadrilateral
Quadrilateral inscribed in a circle
Cyclic quadrilateral
Area of circle with ciclic quadrilateral
Radius of a circle with cyclic quadrilateral
Ptolemy theorem in cyclic quadrilateral
Area of a circle inscribed in a quadrilateral (cyclic quadrilateral circumscribed a circle)
Radius of a circle inscribed in a quadrilateral (Cyclic Quadrilateral)
POLYGON
Sum of interior angle
POLYGON
Size of interior angle
POLYGON
Sum of exterior angle
S = 360 degrees
POLYGON
Size of exterior angle
POLYGON
Number of Diagonals
Area of a regular polygon
Perimeter of a regular polygon
P=n(side)
area of quadrilateral approximation
a line from the center of a regular polygon at right angles to any of its sides
Apothem
Name the common regular polygons from 3 to 20 sides
name common regular polygons from 20 to 100 with increments of 10 (20, 30, 40, …, 100)
Cube
Volume:
Surface Area:
Space Diagonal:
Rectangular Parallelepiped
Volume:
Surface Area:
Space Diagonal:
Right Cylinder
Volume:
Surface Area:
Lateral Area:
Right Cone
Volume:
Surface Area:
Lateral Area:
Right Pyramid
Volume:
Surface Area:
Lateral Area:
(shortcut) Percent increase from single dimension to square dimension:
(shortcut) Percent increase from square dimension to single dimension:
(shortcut) Percent increase from single dimension to cube dimension:
(shortcut) Percent increase from double dimension to cube dimension:
Right Frustrum
Volume:
Surface Area:
Lateral Area:
Sphere
Volume:
Surface Area:
Formula for zone
Spherical Segment (1 base)
Volume:
Surface Area:
Spherical Sector/Spherical Cone
Volume:
Spherical Wedge
Volume:
Spherical lune surface area
polyhedron four equal faces of equilateral triangle
tetrahedron
Tetrahedron
# of faces:
# of vertices:
# of edges:
Euler’s Equation:
Tetrahedron
Total Surface Area:
Volume:
Radius of inscribed sphere:
six square equal faces polyhedron
hexahedron
Hexahedron
# of faces:
# of vertices:
# of edges:
Euler’s Equation:
f = 6
v = 8
e = 12
f + v - e = 2
Hexahedron
Total surface area:
Volume:
Radius of inscribed sphere:
Eight equilateral triangle faces polyhedron
octahedron
Octahedron:
# of faces:
# of vertices:
# of edges:
Euler’s Equation:
f = 8
v = 6
e = 12
f + v - e = 2
Octahedron
Total Surface Area:
Volume:
Radius of Inscribed Sphere:
Dodecahedron
No. of faces:
No. of vertices:
No. of edges:
Euler’s Equation
12 equal pentagon faces of polyhedron
Dodecahedron
Dodecahedron
Total Surface Area:
Volume:
Radius of inscribed sphere:
twenty quadrilateral triangle faces of polyhedron
Icosahedron
Icosahedron
No. of faces:
No. of vertices:
No of edges:
Euler’s Equation:
Icosahedron
Total Surface Area:
Volume:
Radius of inscribed sphere: