Trigonometric Functions University of Texas at （三角函数德克萨斯大学）.pdf

Trigonometric Functions By Daria Eiteneer Topics Covered: Reminder: relationship between degrees and radians The unit circle Definitions of trigonometric functions for a right triangle Definitions of trigonometric functions for a unit circle Exact values for trigonometric functions of most commonly used angles Trigonometric functions of any angle θ in terms of angle θ in quadrant I Trigonometric functions of negative angles Some useful relationships among trigonometric functions Double angle formulas Half angle formulas Angle addition formulas Sum, difference and product of trigonometric functions Graphs of trigonometric functions Inverse trigonometric functions Principal values for inverse trigonometric functions Relations between inverse trigonometric functions Graphs of inverse trigonometric functions Using trigonometric functions: components of a vector Using trigonometric functions: phase shift of a wave Derivatives of trigonometric functions Note: All figures, unless otherwise specified, have a permission to be copied, distributed and/or modified under the terms of the GNU Free Documentation License, Version 1.2 or later. Reminder: Relationship Between Degrees and Radians A radian is defined as an angle θ subtended at the center of a circle for which the arc length is equal to the radius of that circle (see Fig.1). Fig.1. Definition of a radian. The circumference of the circle is equal to 2πR, where R is the radius of the circle. Consequently, 360°=2π radians. Thus, 1 radian=360°/2π ≈ 57.296° 1° = (2π/360) radians ≈ 0.01745 radians The Unit Circle In mathematics, a unit circle is defined as a circle with a radius of 1. Often, especially in applications to trigonometry, the unit circle is centered at the origin (0,0) in the coordinate pla