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Angles in Standard Position

Angles in Standard Position. P(x,y). a). b). d). c). e). f). 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. Terminal arm.

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Angles in Standard Position

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  1. Angles in Standard Position

  2. P(x,y) a) b) d) c) e) f) 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. Terminal arm Sketch the following angles in Standard Position. Initial arm

  3. a) b) c) NOTE: If is any angle, than any angle co-terminal to is represented by a) b) 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. Example #2: Write an expression for the family of angles co-terminal to each of the following.

  4. 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

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

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

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

  8. Form ative Assignment Questions: 1-17,19,20 from Check your understanding in handout

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