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Lecture 1

# MTH 108 Lecture 1: 5.1 Angles and Their Measures Notes - Day 1 of 2 Premium

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School
Department
Mathematics
Course
MTH 108
Professor
Lun- Yi Tsai
Semester
Fall

Description
MTH 108 Precalculus Mathematics II 5.1 Angles and Their Measures Notes Day 1 of 2 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 ▯ Angle’s Standard Positions ▯’s is normally going to be in standard position. What is ▯ is positive? If ▯ is positive, then all of the degrees will be above ▯ . What is ▯ is negative? ▯ If ▯ is negative, then all of the degrees will be below ▯ . 1 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 . 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 2Revolution 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: ▯ 0 1 = 60 = 3600" Minutes to Degrees One minute is equivalent to1 degrees, which can be explained by the following: 60 ▯ ▯ ▯ 0 1 ▯ 1 = 60" = ▯ 0:0167 60 Seconds
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