Trigonometry 1st Qtr June 23, 2008

Angle Measurement
standard method of measurement and conversion

1. Revolution System
> depend on rotation on the axis
> old method
2. Sexagesimal System
> the basic unit is degree ( 1 degree)
3. Radian System
> radium
> radius of a circle
> unit less number

CONVERSION
> degree to radian, the conversion factor is pi/180.
> radian to degree, the conversion factor is 180/pi.

i.e.
1. express 3pi/5 to degree = 3pi/5 * 180/pi = 108 degrees

2. express 255 degrees to radian = 255 degrees * pi/180 = 51pi/36 = 17pi/12

FRACTIONAL DEGREE
1. DD (Decimal Degree)
2. DMS (Degree, Minutes, Seconds)

CONVERSION FACTOR
1 degree = 60 minutes
1 minute = 60 seconds

FBI
(Fabulous Basic Information)
What is a triangle?
> 3 sided polygon that have 3 interior angles
> the sum of the interior angles is always 180 degrees
> used CAPITAL letter for vertices, small letters for legs

Classifications of triangles:
> Acute triangles can be scalene and equilateral, but not an isoceles.
> Obtuse triangles can be scalene and isoceles, but not equilateral.
> Right triangles can be scalene and isoceles, but not equilateral.

Isoceles - 2 sides equal
Scalene - no equal sides
Equilateral - all 3 sides equal

TRIGONOMETRIC RATIO

SOH sin X = opposite/hypotenuse sine function

CAH cos X = adjacent/hypotenuse cosine function

TOA tan X = opposite/adjacent tangent function

To determine the hypotenuse
> longest leg
> opposite of the 90 degree vertex

TRIGONOMETRIC FUNCTIONS of a RIGHT TRIANGLE
sine (sin) -> cosecant (csc)
cosine (cos) -> secant (sec)
tangent (tan) -> cotangent (cot)

QUOTIENT IDENTITY
tan = identical to sin/cos

PYTHAGOREAN THEOREM
> sum of the square of the legs is equal to the square of the longest side, the hypotenuse