[b]1)[color=#ff00ff] The pink angle measures 30 degrees = pi/6 radians. [/color][color=#38761d]The green angle measures 45 degrees = pi/4 radians. [br][/color][/b][br]2) This applet illustrates (what many texts refer to as) "reference triangles" for angles (drawn in standard position) are multiples of [b][color=#ff00ff]30 degrees = pi/6 radians [/color]and [color=#38761d]45 degrees = pi/4 radians. [/color][/b][br][br]3) The [color=#6aa84f][b]light green[/b][/color] and [color=#bf9000][b]manila-colored[/b][/color] reference triangles are 30-60-90 triangles. Each [b][color=#8e7cc3]purple[/color][/b] reference triangle is a 45-45-90 triangle. [br][br]4) The [color=#9900ff][b]hypotenuse[/b][/color] of a 30-60-90 triangle is [b][color=#9900ff]double the length[/color][/b] of the triangle's [color=#9900ff][b]shorter leg[/b][/color]. The[b] legs [/b]of a 45-45-90 triangle [b]are equal.[/b] [br][br]5) Values of the six main trigonometric functions evaluated at the angles described in (2) can be determined from this diagram. (Ex: sin(30 deg) = y/r = 1/2. Also, tan(45 deg) = y/x = 1).