(1,0) (0,1) (-1,0) (0, -1) α (x,y) x y 1 sin(α) = y cos(α) = x (cos(α), sin(α)) (0,0) tan(α) =...
TRANSCRIPT
Chapter 2
Trigonometric Functions
•(1,0)
•(0,1)
•(-1,0)
•(0, -1)
α
•(x,y)
x
y1
sin(α) = y
cos(α) = x
(cos(α) , sin(α))
(0,0)•
tan(α) = y/x
2.1 Unit Circle
-10 -5 5 10
DA
10
60°70°
80°100°110°
120°
130°
150°
160°
170°
190°
200°
210°
220°
230°
240°250°
280°290°
300°
310°
.2 .4 .6 .8 1-1 -.8 -.6 -.4 -.2
.2
.4
.6
.8
1
-.2
-.4
-.6
-.8
-1
10°
20°
30°
40°
50°
140°
260°
320°
330°
340°
350°
• 10°
• 20°• 30°
• 40° •
• • • • •
•
••
•
• 350°•
• 340°•• 330°•
••
• 320° •
• • •
••
• • •
50°60°
70°80°100°110°120°
130°140°
150°160°
170°
190°
200°
210°
220°230°
240°250°
260° 280°290°
300°310°
.2 .4 .6 .8 1-1 -.8 -.6 -.4 -.2
.2
.4
.6
.8
1
-.2
-.4
-.6
-.8
-1
Quadrant IQuadrant II
Quadrant III Quadrant IV
Sine +Cosine +Tangent +
Sine +Cosine -Tangent -
Sine -Cosine -Tangent +
Sine -Cosine +Tangent -
2.2 Arc Length and Sectors
d(1/7)d
C = πd
2.2 Arc Length and Sectors
• r
r 2r 2
r 2
(1/7) r 2
A = πr 2
α•
2.2 Arc Length and Sectors
s
α s 360 πd =
50°•
2.2 Arc Length and Sectors
s
α s 360 πd =
20 in.
50°•
2.2 Arc Length and Sectors
s
50 s 360 40π=
20 in.
200π 360
=
= 1.74 in.
α•
2.2 Arc Length and Sectors
k
α k 360 πr = 2
45°•
2.2 Arc Length and Sectors
k
α k 360 πr = 2
6 ft.
45 k 360 36π
=
K = 14.14 in. 2
2.3 Radian Measure
0 rad.π rad. 2π rad.
1 rad.2 rad.
3 rad.
4 rad. 5 rad.
6 rad.
π 2
rad.
3π 2
rad.
60°70°
80°100°110°
120°
130°
150°
160°
170°
190°
200°
210°
220°
230°
240°250°
280°290°
300°
310°
10°
20°
30°
40°
50°
140°
260°
320°
330°
340°
350°
π 180° 0, 2π
π 2
3π 2
π 6
5π 6
2.4 Inverse Trig Functions and Negative Angles
sin (.6) = _____________─ 1 36.87˚
-10 -5 5 10
DA
10
60°70°
80°100°110°
120°
130°
150°
160°
170°
190°
200°
210°
220°
230°
240°250°
280°290°
300°
310°
.2 .4 .6 .8 1-1 -.8 -.6 -.4 -.2
.2
.4
.6
.8
1
-.2
-.4
-.6
-.8
-1
10°
20°
30°
40°
50°
140°
260°
320°
330°
340°
350°
2.4 Inverse Trig Functions and Negative Angles
sin (.6) = ____________________─ 1 36.87˚ or 143.13˚
36.87˚ + 360n143.13˚ + 360n
2.4 Inverse Trig Functions and Negative Angles
cos (.4) = ____________________─ 1 66.42˚
-10 -5 5 10
DA
10
60°70°
80°100°110°
120°
130°
150°
160°
170°
190°
200°
210°
220°
230°
240°250°
280°290°
300°
310°
.2 .4 .6 .8 1-1 -.8 -.6 -.4 -.2
.2
.4
.6
.8
1
-.2
-.4
-.6
-.8
-1
10°
20°
30°
40°
50°
140°
260°
320°
330°
340°
350°
2.4 Inverse Trig Functions and Negative Angles
cos (.4) = ____________________─ 1 66.42˚ or 293.58˚
66.42˚ + 360n293.58˚ + 360n
2.4 Inverse Trig Functions and Negative Angles
tan (2.5) = _____________─ 1 68.2˚
-10 -5 5 10
DA
10
60°70°
80°100°110°
120°
130°
150°
160°
170°
190°
200°
210°
220°
230°
240°250°
280°290°
300°
310°
.2 .4 .6 .8 1-1 -.8 -.6 -.4 -.2
.2
.4
.6
.8
1
-.2
-.4
-.6
-.8
-1
10°
20°
30°
40°
50°
140°
260°
320°
330°
340°
350°
2.4 Inverse Trig Functions and Negative Angles
tan (2.5) = ____________________─ 1 68. 2˚ or 248.2˚
68.2˚ + 180n