MATH117 Lecture Notes - Lecture 7: Radian, Unit Circle, List Of Trigonometric Identities
19 Oct 2017
School
Department
Course
Professor
Document Summary
7 the trigonometric functions (a. k. a. the circular functions) De nition: one radian is the angle for which the length of the arc of a circle matches the radius of that circle. The radian measure of an angle is the ratio of arc length to radius (in any circle drawn with the vertex of the angle at its center): = s r. Well, we know that the circumference of a circle (that is, the arc length for a full circle) is s = 2 r. Matching this to the formula s = r , we discover that in a full circle, = 2 radians. Hence 2 radians = 360 , which allows us to conclude that 1 rad = 180. To make you a bit more comfortable with radian measure, it may help to note that 1 radian 57. 3 . Since they are de ned by a ratio of lengths, they are dimensionless.
in a circle of radius 2.5 cm is subtended by an arc of length 7 cm. Find the measure of in degrees and radians.
