4.1--Angles and Their Measures Convert to degrees, minutes, and seconds (DMS): o 1) 47.15 o 2) 129.62 Convert from DMS to decimal form: 3) 151o 52' 24" 4) 21o 16' 30" ~What exactly is a radian ???? 4.1--Angles and Their Measures 5) Convert from degrees to radians: o 36 o 150 o 240 o 75.4 o 128 42' 6) Convert from radians to degrees: π 9 5π 12 11π 30 3 4.7 4.1--Angles and Their Measures 7) Find the perimeter of the shaded region to the nearest 1/10th of an inch: 8) A circular pool is encircled by a concrete path. The circumference of the outer edge of the path is 33.3 feet longer than that of the w inner edge. How wide is the path? (Round to the nearest 1/10th of a foot.) 4.1--Angles and Their Measures 9) Find the angle in degrees that describes each compass bearing: N SW W E ENE SSE S 10) Which compass direction NOTE: Compass bearings is closest to 250 ? are measured differently than the unit circle is ! 11) The wheels on a car are 32" in diameter. If these wheels are turning at 700 revolutions per minute, find the car's speed: 4.1--Angles and Their Measures 12) The chain of the bicycle wraps around circles of radius 8" and 3" as shown in the diagram. The angular speed of the smaller wheel is 90 RPM. a) Convert the angular speed of the smaller wheel to radians per second. 8" 3" b) Find the linear speed of the chain in inches per second. c) Find the angular speed of the larger wheel in radians per second. 1 statute (land) mile = 5280 feet 1 nautical mile = 1' of the earth's circumference measured at the equator Conversions: 1 statute mile = 0.87 nautical miles 1 nautical mile = 1.15 statute miles Perform the following conversions: 13) 41.2 nautical miles = statute miles 14) 350 statute miles = nautical miles.