Notes 4.1 – Angles and Their Measure

I. Angle Measure Each degree is divided into 60 minutes and each minute is divided into 60 seconds

B.) Ex.- Convert 65.875º to DMS (Degrees/Minutes/Seconds)

C.) Ex.- Convert 135º 28’ 42’’ to decimal degrees.

II. Course and Bearing A.) Def: The angle, measured clockwise, between due North and the line of travel B.) Graphically:

III. Radian Measure A.) Def: A central angle of a circle has a measure of 1 RADIAN if it intercepts an arc with the same length as the radius. a

B.) Conversions: 1.) Radians to degrees : 2.) Degrees to radians :

C.) Ex.- Convert the following degree measures to radians.

D.) Ex.- Convert the following degree measures to radians.

IV. Arc Length A.) Def: If θ is a central angle of a circle with radius r and θ is measured in radians, then the arc length s is given by B.) If θ is in degrees:

C.) Ex.- Find the perimeter of a slice pizza from a large pie (8 slices) if it has an 8 inch radius.

V. Linear Motion A.) Angular speed = revolutions per minute B.) Linear speed = miles per hour 1 radian = 1 radius

C. ) Ex. Find the speed of a truck with wheels 36 in C.) Ex. Find the speed of a truck with wheels 36 in. in diameter that are rotating at 630 rpm (revolutions per minute).

VI. Statute vs. Nautical Miles 1 Statute mile ≈ 0.869 Nautical mile 1 Nautical mile ≈ 1.151 Statute miles