Download 2-1 Angles in the Cartesian Plane

January 21, 2015
2-1
Angles in the
Cartesian Plane
Standard Position
An angle is said to be in standard position if its initial side is along
the positive x-axis and its vertex is at the origin
terminal side
vertex
(0, 0)
Let's label each quadrant
and mark what angle occurs
at each axis
initial side
Example 1
State in which quadrant or on which axis each of the following angles
with given measure in standard position would lie.
a) 91º
b) 175º
c) 180º
d) -475º
e) -630º
Example 2
Coterminal Angles
Sketch each of the following angles in standard position.
Two angles in standard position with the same terminal side
a) 225º
Examples:
b) 135º
c) -330º
d) -720º
-40º and 320º
60º and 420º
150º and 510º
220º and 580º
January 21, 2015
Example 3
Determine the angle of the smallest possible positive measure that is
coterminal with each of the following angles.
a) 379º
b) -187º
c) 945º
d) 360º
e) 1395º
2-2
Definition 2 of the
Trigonometric
Functions: The
Cartesian Plane
Trigonometric Functions
Example 1
point (x, y) to the origin; then the six trigonometric functions are
defined as:
The terminal side of an angle Θ in standard position passes through the
indicated point. Calculate the values of the six trigonometric functions
for each angle Θ.
b) (-1, 3)
a) (8, 4)
Let (x, y) be any point, other than the origin, on the terminal side
of an angle Θ in standard position. Let r be the distance from the
sin Θ = cos Θ =
tan Θ =
csc Θ = sec Θ =
cot Θ =
Example 1 (cont.)
Example 2
The terminal side of an angle Θ in standard position passes through the
indicated point. Calculate the values of the six trigonometric functions
for each angle Θ.
Calculate the values for the six trigonometric functions for the angle Θ
given in standard position.
e) (0, 1)
f) (-1, 0)
a) 720º
January 21, 2015
Calculate the values for the six trigonometric functions for the angle Θ
given in standard position.
Example 1 (cont.)
The terminal side of an angle Θ in standard position passes through the
indicated point. Calculate the values of the six trigonometric functions
for each angle Θ.
b) -90º
c)
d)