Definition: an angle is in standard position when its INITIAL ARM is on the x-axis and the angles vertex is at the origin.(0,0) Point P(x,y) is a point on the TERMINAL ARM of the angle. P(x,y) Initial arm Terminal arm Sketch the following angles in Standard Position. a) b) c)d) e)f)

Definition: angles which have the same terminal arm are called CO-TERMINAL Angles. Example #1: Calculate two angles co-terminal to each angle below. Make one positive and one negative. a)b) c) NOTE NOTE: If is any angle, than any angle co-terminal to is represented by Example #2: Write an expression for the family of angles co- terminal to each of the following. a) b)

Definition: for any angle in standard position, its reference angle is the ACUTE angle between its terminal arm and the X- AXIS. Example: For an angle of the reference angle is Reference Angle

For each of the following, sketch the angle in standard position, find and label the reference angle. a)b) c) d) e)

SinCosTan

Solve the Following Triangles (answers must be exact values) A B C D E F 8cm

Example: Given P(3,-4) on the terminal arm of angle, find the primary trig ratios. P(3,-4) 3 -4 Find the length of the hypotenuse.

Questions: 1-17,19,20 from Check your understanding in handout