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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
Radian Measure
6
Definition of Radians
C 2pr
C 2p radii
C 2p radians
360o 2p radians
r
180o p radians
1 Radian ? 57.3 o
r
7
Unit Circle Radian Measure
8
Unit Circle Radian Measure
9
Unit Circle Radian Measure
Degrees
10
Converting Degrees ? Radians
Converts degrees to Radians
Recall
Converts Radians to degrees
more examples
11
Trigonometric Ratios
12
Basic ratio definitions
Hypotenuse
Opposite Leg
Reference Angle
?
Adjacent Leg
13
Circle Trigonometry Definitions
(x, y)
Radius r
Opposite Leg y
Adjacent Leg x
reciprocal functions
14
Unit - Circle Trigonometry Definitions
(x, y)
Radius 1
Opposite Leg y
Adjacent Leg x
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)
Quadrant Angles
(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
Unit Circle Radian Measure
sin
cos
tan
(-, )
(, )
Quadrant Angles
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
2nd Quadrant Angles
3rd Quadrant Angles
4th Quadrant Angles
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
Quadrant Angles
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)
Radius r
Opposite Leg y
Adjacent Leg x
return
37
Unit Circle Radian Measure
1
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