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## Trigonometry

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### Unit Circle Degree Measure ... (x, y) Radius = r Adjacent Leg = x Opposite Leg = y reciprocal functions Unit - Circle Trigonometry Definitions (x, y) ... – PowerPoint PPT presentation

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Title: Trigonometry

1
Trigonometry
?
2
Definition of an angle
Terminal Ray
Counter clockwise
Initial Ray
- clockwise
Terminal Ray
3
Coterminal angles angles with a common terminal
ray
Terminal Ray
Initial Ray
4
Coterminal angles angles with a common terminal
ray
Terminal Ray
Initial Ray
5
6
C 2pr
r
r
7
8
9
Degrees
10
Recall
more examples
11
Trigonometric Ratios
12
Basic ratio definitions
Hypotenuse
Opposite Leg
Reference Angle
?
13
Circle Trigonometry Definitions
(x, y)
Opposite Leg y
reciprocal functions
14
Unit - Circle Trigonometry Definitions
(x, y)
Opposite Leg y
1
15
Unit Circle Trig Ratios
sin
cos
tan
(, )
(-, )
(, -)
(-, -)
Skip p/4s
Reference Angles
16
Unit Circle Trig Ratios
sin
cos
tan
(, )
(-, )
(-, -)
(, -)
17
Unit Circle Trig Ratios
sin
cos
tan
(, )
(-, )
(0 , 1)
(1, 0)
(-1, 0)
sin
cos
tan
0
/2p
1
0
0
0
Ø
1
(0, -1)
(-, -)
(, -)
0
-1
0
Ø
-1
0
View p/4s
18
sin
cos
tan
(-, )
(, )
sin
cos
tan
1
0
/2p
1
0
0
0
Ø
1
(-, -)
(, -)
0
-1
0
Ø
Degrees
-1
0
19
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20
Graphing Trig Functions
f ( x ) A sin bx
21
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22
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23
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24
Amplitude is the height of graph measured from
middle of the wave.
Amplitude
Center of wave
f ( x ) A sin bx
25
f ( x ) cos x
A ½ , half as tall
26
f ( x ) sin x
A 2, twice as tall
27
Period of graph is distance along horizontal axis
for graph to repeat (length of one cycle)
f ( x ) A sin bx
28
f ( x ) sin x
B ½ , period is 4p
29
f ( x ) cos x
B 2, period is p
30
A unit circle is a circle with a radius of 1
unit. For every point P(x, y) on the unit circle,
the value of r is 1. Therefore, for an angle ? in
the standard position
31
The End
Trigonometry Hipparchus, Menelaus, Ptolemy
Special Right Triangles The Pythagoreans
Graphs Rene DesCartes
32
Reference Angle Calculation
Return
33
Unit Circle Degree Measure
90
120
60
135
45
150
30
0/360
180
330
210
225
315
300
240
270
Return
34
Unit Circle Degree Measure
sin
cos
tan
30
90
(-, )
(, )
45
120
60
135
45
60
150
30
0/360
180
sin
cos
tan
1
330
210
0/360
1
0
0
225
315
0
Ø
1
90
300
240
(-, -)
(, -)
0
-1
0
180
270
Ø
Return
-1
0
270
35
Ex. 4
Ex. 3
Ex. 6
Ex. 5
return
36
Circle Trigonometry Definitions Reciprocal
Functions
(x, y)