13.2 - Define General Angles and Radian Measure Page 856 3) 5) 7) 9) 11) 13) 15) C 17) x = 8√3, y = 16 19) x = 4√3, y = 8√3 21) B = 55°, a ≈ 9.177, b ≈ 13.106 23) A = 72°, a ≈ 22.825, b ≈ 7.416 25) A = 15°, b ≈ 55.981, c ≈ 57.956 27) B = 26°, a ≈ 65.610, c ≈ 72.998 32) Height: 100.263 ft, Length: 170.577 ft 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

13.2 - Define General Angles and Radian Measure 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

Define General Angles and Radian Measure Section 13.2 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

13.2 - Define General Angles and Radian Measure Definitions Angle of Rotation is formed by two rays with a common endpoint, also called the vertex. One ray is called the initial side. The other ray is called the terminal side. The measure of the angle is determined by the amount and direction of rotation from the initial side to the terminal side. Coterminal angles are angles in standard position with the same terminal side To determine the coterminal angles, add and/or subtract 360° (Magic Number is 360°) Coterminal angles can be negative There are an infinite amount of coterminal angles 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

13.2 - Define General Angles and Radian Measure Example 1 Draw 210° with the given measure in standard position. Then, determine which quadrant the terminal side lies. Label the axis when drawing angles Must draw the angle and its arrow (to indicate both the direction) receive full credit 210° 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

13.2 - Define General Angles and Radian Measure Example 2 Draw –45° with the given measure in standard position. Then, determine in which quadrant the terminal side lies. –45° 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

13.2 - Define General Angles and Radian Measure Example 3 Draw 510° with the given measure in standard position. Then, determine in which quadrant the terminal side lies. Get the actual angle 510° - 360° = 150° So the terminal side makes 1 complete revolution and continues another 150°. 150° 510° 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

13.2 - Define General Angles and Radian Measure Your Turn Draw 400° with the given measure in standard position. Then, determine in which quadrant the terminal side lies. 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

13.2 - Define General Angles and Radian Measure Example 4 Find the measures of a positive and negative angles that are coterminal with ө = 40°. Magic Number: 360° 40° 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

13.2 - Define General Angles and Radian Measure Example 5 Find the measures of a positive and negative angles that are coterminal with ө = 65° 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

13.2 - Define General Angles and Radian Measure Your Turn Find the measures of a positive and negative angles that are coterminal with ө = 740° 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

13.2 - Define General Angles and Radian Measure Degree measure is a unit of application such as surveying and navigation Radian measure is a unit of measure for theoretical work in mathematics. Before angles, they measured in Radian Measure One radian is the measure of an angle in standard position whose terminal side intercepts an arc of length, r. r r one radian 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

13.2 - Define General Angles and Radian Measure Conversions To convert degrees to radians, multiply π/180° To convert radians to degrees, multiply 180°/π 180° = π Radian 1° = π/180 Radian 180°/π = 1 Radian 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

13.2 - Define General Angles and Radian Measure Example 6 Convert 240° into radian measure 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

13.2 - Define General Angles and Radian Measure Example 7 Convert –90° into radian measure 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

13.2 - Define General Angles and Radian Measure Your Turn Convert 2° into radian measure 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

13.2 - Define General Angles and Radian Measure Example 8 Convert 9π/2 into degree measure 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

13.2 - Define General Angles and Radian Measure Example 9 Convert 1 Radian into degree measure 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

Arc Length and Area of Sector Sector is a region of the circle that bounded by two radii and an arc of a circle The Central Angle of a sector is the angle formed by the two radii Arc Length equation: s = r ө Area of a Sector: A = (r2ө)/2 Degrees must be converted to Radians Arc Length, s 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

13.2 - Define General Angles and Radian Measure Example 10 Determine the Arc Length and Area of Sector with the given radius of r = 4 inches and ө = π/6. 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

13.2 - Define General Angles and Radian Measure Example 11 Determine the Arc Length and Area of Sector with the given radius of r = 15 inches and ө = 45°. 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

13.2 - Define General Angles and Radian Measure Example 12 Determine the Arc Length and Area of Sector with the given radius of r = 180 feet and ө = 90°. 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

13.2 - Define General Angles and Radian Measure Your Turn Determine the Arc Length and Area of Sector with the given radius of r = 8 inches and ө = 115°. 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure

13.2 - Define General Angles and Radian Measure Assignment Page 862 3-37 odd, 33-37 leave π form 1/3/2019 9:22 AM 13.2 - Define General Angles and Radian Measure