5.1 Angles in standard position in quadrant 1

  • r in term of x and y
  • the value ofθin terms of x and y
  •  the x-coordinate of P in terms of r andθ
  • the y-coordinate of P in terms of r and θ

 

The coordinates of a point P on the coordinate plane can be described by its distance r from the origin, O, and the angleθthat Op makes with the positive x-axis. When the angle θ, between 0and 360 is measured counter clockwise from the positive x-axis, the angle is in standard position. The ray OP is the terminal arm of the angle and the oint P is a terminal point for the angle.

 

Trigonometry is essential to navigation. A direction can be described by relating it to two of the compass points: north, south, west and east.

ex) a heading of W30S means from a direction due west, rotate 30 counter clockwise; that is, toward south.

ex)a heading of W40N means from a direction due west, rotate40 clockwise; that is, toward north.

 

5.2 Angles in standard position in all quadrant

The terminal arm of an angle in quadrant 1 can be successively reflected in both axes to form 4 different angles in standard position. The reference angles in standard position. The reference angle for all angles is the acute angle that the terminal arm makes with the x-axis.

 

In Lesson 5.1, the trigonometric ratios of an angle in standard position in Quadrant 1 were related to the coordinates of a point on the terminal arm of the angle. These relationships can be extended to define the primary trigonometric ratios for any angle θ  in standard position. For angles greater than 90, a represents the reference angle.