4.1 Radian and Degree Measure started.notebook January 10, 2012 4.1 Radian and Degree Measure standard postition terminal side angle positive angle negative angle vertex initial side coterminal 1 4.1 Radian and Degree Measure started.notebook January 10, 2012 terminal side angle positive angle initial side negative angle coterminal angle initial side terminal side vertex standard postition vertex 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 2 4.1 Radian and Degree Measure started.notebook January 10, 2012 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 or: θ= s = r θ Must be in RADIANS 3 4.1 Radian and Degree Measure started.notebook January 10, 2012 4 4.1 Radian and Degree Measure started.notebook January 10, 2012 Degrees Radians Full revolution Half revolution Acute angles Obtuse angles Complementary angles Supplementary angles 5 4.1 Radian and Degree Measure started.notebook January 10, 2012 Two positive angles and are complementary if their sum is... Two positive angles are supplementary if their sum is... 6 4.1 Radian and Degree Measure started.notebook January 10, 2012 a. Find the complement and supplement of: π/4 b. Find the complement and supplement of: 4π/5 7 4.1 Radian and Degree Measure started.notebook coterminal angles January 10, 2012 Find 2 angles, one positive and one negative, coterminal to: 50 degrees 40 degrees π/8 -π/5 8 4.1 Radian and Degree Measure started.notebook January 10, 2012 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) 9 4.1 Radian and Degree Measure started.notebook January 10, 2012 Applications of Angles Arclength: s = linear speed = arclength s or t time linear speed is how fast the particle moves angular speed = ø t angular speed is how fast the angle changes 10 4.1 Radian and Degree Measure started.notebook January 10, 2012 1. Find the radian measure of the central angle of a circle of radius 22ft that intercepts an arc of length 10ft 2. Find the length of the arc on a circle with a radius 9ft intercepted by a central angle 60o 11 4.1 Radian and Degree Measure started.notebook January 10, 2012 A 6inchdiameter front gear on a bicycle makes 2.5 revolutions per second. Find the angular speed of the gear in radians per second. 12 4.1 Radian and Degree Measure started.notebook January 10, 2012 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 13 4.1 Radian and Degree Measure started.notebook January 10, 2012 Find the distance between Johannesburg, South Africa, (latitude 26o 11' S) and Jerusalem, Israel (latitude 31o 47' N). Assume that the earth is a sphere of radius 4000 miles, and the cities are on the same longitude (due north of each other) 14 4.1 Radian and Degree Measure started.notebook January 10, 2012 15
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