Section+4.3+Trigonometric+Functions+of+Angles

Section 4.3 Trigonometric Functions of Angles Definition: Trigonometric Functions - Let (x,y) be a point, other than the origin, on the terminal side of an angle theta in standard position. Let r be the distance from the point (x,y) to the origin. Then the six trigonometric functions are defined as Sin(0) = y/r Cos(0) = x/r Tan(0) = y/x Csc(0) = r/y Sec(0) = r/x Cot(0) = x/y where r = square root of x^2 +y^2, or x^2 + y^2 = r^2 - Ranges of the Trigonometric Functions For any angle theta for which the trigonometric functions are defined, the six trigonometric functions have the following ranges: -1 < sin 0 <1 -1 < cos0 <1 Sec0 < -1 or Sec0 >1 Csc0 < 1 or Csc0 >1 Defintion: Reference Angle - For angle theta 0 degress < theta < 360 degrees < 2pi, in standard position whose terminal side lies in one of the four quadrants, there exists a reference angle x, which is the acute angle formed by the terminal side of angle theta and the x-axis. Definition: Reference Right Triangle - To form a reference right triangle for angle theta, where 0 degrees < theta < 360 degrees or 0 < theta < 2pi, drop a perpindicular line from the terminal side of the angle to the x-axis. The right triangle now has reference angle x as one of its acute angles.
 * I. Trigonometric Functions: The Cartesian Plane**
 * II. Ranges of the Trigonometric Functions**
 * III. Refrence Angles and Triangles**