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MTH 108 Quiz: Chapter 5 Study Guide Notes
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Department
Mathematics
Course
MTH 108
Professor
Lun- Yi Tsai
Semester
Fall

Description
MTH 108 Precalculus Mathematics II Chapter 5 Study Guide Notes L. Sterling Abstract Provide a generalization to each of the key terms listed in this section. Ray What is a ray? A ray, which can also be classified as a “half-line”, is a line that has only one end; rays start at one given point, which can also be called an "endpoint", and then it extends to any direction forever, which can be considered as "going to infinity". Initial and Terminal Sides What is the difference between an initial and terminal side? Initial Sides ▯ Initial sides are normally half-lines that are at 0 with a vertex while holding the given half-line in place. Terminal Sides Terminal sides are normally rotating to determine either a positive or negative angle, which can be explained by the following: Counterclockwise Positive Clockwise Negative Angle ▯ Quadrant Angles Lying in Quadrant I ▯ ▯ ▯ must be in the first quadrant iff (if and only if) ▯ is between 0 and 90 . Lying in Quadrant II ▯ ▯ ▯ must be in the second quadrant iff (if and only if) ▯ is between 90 and 180 . Lying in Quadrant III ▯ must be in the third quadrant iff (if and only if) ▯ is between 180 and 270 . Quadrantal Angle ▯ must be the quadrantal angle iff (if and only if) ▯ is exactly 270 . 1 Lying in Quadrant IV ▯ must be in the first quadrant iff (if and only if) ▯ is between 270 and 360 . Revolutions ▯ ▯ ▯ ▯ 90 180 270 360 Right Angle Straight Angle Right Angle Straight Angle 1 1 3 4Revolution 2 Revolution 4Revolution 1 Revolution Counterclockwise Counterclockwise Counterclockwise Counterclockwise Conversions Degrees to Minutes to Seconds One degree can be equivalent to 60 minutes, which is also equivalent to 3600 seconds, which can be explained by the following: 1 = 60 = 3600" Minutes to Degrees 1 One minute is equivalent t60 degrees, which can be explained by the following: ▯ ▯ ▯ 1 = 60" = 1 ▯ 0:0167 ▯ 60 Seconds to Degrees One second is equivalent to1 degrees, which can be explained by the following: 3600 ▯ ▯ ▯ ▯ ▯ ▯ 1 0 1 1 ▯ 1 ▯ ▯ 1 = = ▯ = ▯ 0:0002778 60 60 60 3600 Degrees, Minutes, and Seconds When you have degrees, which is normally d, minutes, which is normally m, and seconds, which is normally s, can be expressed by the following: d m s" Decimal Degrees m s One decimal degree, which is normally dd, is equivalent to degree60plus 3600, which can be explained by the following: m s dd = d + 60 + 3600 Circle’s Arc Length Proportional Ratio The following is the proportional ratio for the arc length: ▯ s = ▯1 s1 2 Arc Length The arc length is when the arc length, which is normally labeled s, is being subtended by the circle’s radius, which is normally labeled r, and its central angle, which is normally labeled with ▯ radians, which is all expressed by the following formulas: s = r▯ Length s Radius r Central Angle ▯ radians Central Angle The central angle is an angle with a vertex being the circle’s center. Conversions Revolutions to Radians 1 Revolution = 2▯ Radians s = 2▯r Degrees to Radians ▯ 1 = Radians 180 180 = ▯ Radians Circle’s Sector Area Proportional Ratio The following is the proportional ratio for the sector area: ▯ = A ▯1 A1 Sector Area The sector area is when half of the circle’s squared radius, which is normally la2r or either r2 2, and its central angle, which is normally labeled with ▯ radians, which is all expressed by the following formulas: 1 2 A = 2 r ▯ Area A Radius r Central Angle ▯ radians Linear and Angular Speed Linear Speed The linear speed, or linear velocity, occurs when the distance, which is normally labeled s, is being traveled in time, which is normally labeled t, around its circle, which would make its speed/velocity, which is normally labeled v, which is all expressed by the following formula: v = s t 3 Angular Speed The angular speed, or angular velocity, occurs when the angle, which is normally labeled !, is when the radians, which is normally labeled ▯, while being divided by its elapsed time, which is normally labeled t, which is all expressed by the following formula: ▯ ! = t Converting Linear and Angular Speed When it comes to linear and angular speed, the linear speed, which is normally labeled v, is equaled to the radians, which is normally labeled r, per unit time multiplied by the angular speed, which is normally labeled !, which is all expressed by the following formula: v = r! ▯ in Degrees and Radians When it comes to the value of a function, that’s trigonometric, of any possible angle would be equaled to the exact same function, that’s also trigonometric, of an angle, which means ▯ in this case, that it coterminal to a given angle. Degrees : 0 ▯ ▯ ▯ 360 ▯ Radians : 0 ▯ ▯ ▯ 2▯ Thanks to the angle, which also means ▯ in this case, and the following where k can be expressed as any integer would be coterminal: Degrees : ▯ + 360 k Radians : ▯ + 2▯k Signs of Trigonometric Functi
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