Download 2-1 Angles in the Cartesian Plane

January 20, 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)
initial side
Example 1
Let's label each quadrant
and mark what angle occurs
at each axis
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
Coterminal Angles
Example 2
Two angles in standard position with the same terminal side
Sketch each of the following angles in standard position.
a) 225º
b) 135º
c) -330º
d) -720º
Examples:
-40º and 320º
60º and 420º
150º and 510º
220º and 580º
January 20, 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
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
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.
point (x, y) to the origin; then the six trigonometric functions are
defined as:
a) (8, 4)
sin Θ = cos Θ =
tan Θ =
csc Θ = sec Θ =
cot Θ =
Example 1
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.
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)
e) (0, 1)
January 20, 2015
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.
f) (-1, 0)
a) 720º
Example 2
Example 1 (cont.)
Calculate the values for the six trigonometric functions for the angle Θ
given in standard position.
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)