4.1 Radian and Degree Measure angle standard postition terminal side coterminal positive angle initial side vertex negative angle Dec 1610:12 PM terminal side positive angle vertex initial side negative angle angle coterminal angle initial side terminal side vertex standard postition standard postition determined by rotating a ray about its endpoint is the starting position of the rotated ray in the formation of an angle. is the position of the ray after the rotation when an angle is formed. is the endpoint of the ray used in the formation of an angle the angle's vertex is at the origin of a coordinate system and its initial side coincides with the positive xaxis positive angle counterclockwise rotation negative angle clockwise rotation coterminal two angles that have the same initial side and the same terminal side Dec 1610:23 PM 1 Radian Measure One radian is the measure of a central angle θ that intercepts an arc s equal in length to the radius r of the circle. 1 Radian ≈ 57 degrees π Radians = 180o Arc Length s = r θ or: θ= Must be in RADIANS Dec 1610:47 PM Dec 1710:40 AM 2 Degrees Radians Full revolution Half revolution Acute angles Obtuse angles Complementary angles Supplementary angles Dec 1611:04 PM Two positive angles and are complementary if their sum is... Two positive angles are supplementary if their sum is... Dec 1710:41 AM 3 a. Find the complement and supplement of: π/4 b. Find the complement and supplement of: 4π/5 Dec 1611:17 PM coterminal angles Find 2 angles, one positive and one negative, coterminal to: 50 degrees 40 degrees π/8 -π/5 Dec 1610:57 PM 4 Convert degrees to radians or radians to degrees MULTIPLY 180 π = 1 = π 180 Convert 120 degrees to radians Convert 5π/6 to degrees Convert 50 degrees to radians Convert π/5 radians to degrees Convert 2 radians (doesn't always have to have in π) Dec 1611:21 PM Applications of Angles Arclength: s = linear speed = arclength s or time t linear speed is how fast the particle moves angular speed = ø t angular speed is how fast the angle changes Dec 179:04 AM 5 A 6inchdiameter front gear on a bicycle makes 2.5 revolutions per second. Find the angular speed of the gear in radians per second. Jan 86:55 AM One more way to measure angles... Do M' S" degrees, minutes (1/60o), seconds (1/3600o) Convert to decimal degree form: 54o 30' 25" Convert to Do M' S" form: 45.279o Jan 86:56 AM 6 Jan 510:02 AM 7
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