Some Trigonometry

Triangles

A triangle has 6 measurements: 3 angles and 3 sides

Angles A+B+C=180 degrees
Sides a,b,c are opposite of their corresponding angles

Law of Sine: sin(A)/a = sin(B)/b = sin(C)/c
Law of Cosine:
a^2 = b^2 + c^2 - 2bc cos(A)
b^2 = a^2 + b^2 - 2ac cos(B)
c^2 = a^2 + b^2 - 2ab cos(C)

Pythagorean Theorem:
when the angle opposite to side c is equal to 90 degrees then..
a^2 + b^2 = c^2

Heron's Formula:
A=squareroot[s(s-a)(s-b)(s-c)] where is the semiperimeter s = (a+b+c)/2

For a right triangle :
sin = opposite/hypotenuse
cos = adjacent/hypotenuse
tan = opposite/adjacent

Area of Triangle:
Known:

Angle Side Angle (ASA) Find 3rd angle: A+B+C=180
Or Side Angle Angle (SAA) Area = (a^2 sin(B) sin(C))/(2 sin(A))

2 Sides and Angle between them (SAS) Area = 1/2 ab sin(C)

2 Sides and Angle not between them (ASS) Find B from: sin(B) = (b sin(A))/a
Find C from: A+B+C=180
Area = 1/2 ab sin(C)

3 Sides (SSS) Use Heron's Formula to find area

Math: Geometry

Area:
Triangle: A=1/2 (base)(height)
Square/rectangle/parallelogram: A=(base)(height)
Trapezoid: A=(Height/2)(base 1 + base 2)
Circle: A=(pi)(radius)^2
Eclipse: A=(pi)(radius 1)(radius 2)

Volume:
Cube/Rectangular Prism: V=(base)(height)(width)
Cylinder: V=(pi)(radius)^2(height)
Cone: V=(1/3)(pi)(radius)^2(height)
Pyramid: V=(1/3)(base)(height)
Sphere: V=(4/3)(Radius)^3
Ellipsoid: V=(4/3)(radius 1)(radius 2)(radius 3)

Circles:
Circumference: C=(pi)(diameter)
Length of Arc: L=(radius)(theta) ... If theta is in radians.
Length of Arc: L=(radius)(pi/180)(theta) ... If theat is in degrees.
Area of Circle piece: A=(theta/360)(pi)(radius)^2 ... If theta is in degrees.
Area of Circle piece: A=(theta/2pi)(pi)(radius)^2