Trig Functions

1
Trig Functions
Angle in Standard Position
2
Trig Functions
From any point on the terminal side
drop a -
3
Trig Functions
xhorizontal distance yvertical distance rdist
from origin to point (r is always positive!)
4
Trig FunctionDefinitions
5
Trig FunctionDefinitions
6
Suppose the point (3,-4) is on the terminal side
of an angle (standard position). Find all six
trig function values.
7
Given x
3
Given y
-4
Calculate r.
Since
r
5
8
Knowing x3, y-4, and r5...
-4/5
3/5
-4/3
9
Knowing x3, y-4, and r5...
-5/4
5/3
-3/4
10
Quadrantal Angles

• terminate on an axis
• measure is a multiple of 90º
• Have trig function values of either 0, 1, -1 or
  undefined

11
Suppose the point (0,3) is on the terminal side
of an angle. Find all six trig function values.
12
Given x
0
Given y
3
Calculate r.
Since
r
3
13
Knowing x0, y3, and r3...
3/3 1
0/3 0
3/0 à undefined
14
Knowing x0, y3, and r3...
3/3 1
3/0 à undefined
0/3 0
15
Given
terminates in
quadrant 3, will the sine value, y/r, be
positive or negative ?
16
Given 1 Trig Ratio ? Find Another

• Given sin ? 4/5
• and ? terminates in Quad 2,
• find cos ?.
• Given tan ? -8/15
• and ? terminates in Quad 4,
• find sin ?.