Θ. + Counter clockwise - clockwise Initial Ray Terminal Ray Definition of an angle.
19
θ sin
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Transcript of Θ. + Counter clockwise - clockwise Initial Ray Terminal Ray Definition of an angle.
θsin
+ Counter clockwise
- clockwise
Initial Ray
Terminal Ray
Terminal Ray
Definition of an angle
Radian Measure
2
,0
2
3
r
r1 Radian
57.3 o
2
360o = 2π radians
180o = π radians
Definition of Radians
C= 2πr
C= 2π radii
C= 2π radians
6
3
2
3
2
6
5
2,0
6
7
3
4
2
3
3
5
6
11
Unit Circle – Radian Measure
61
6
2
6
3
64
65
66
4
2
4
3
2,0
4
5
2
3
4
7
Unit Circle – Radian Measure
44
43
42
41
6
4
3
2
3
2
4
3
6
5
2,0
6
7
4
5
3
4
2
3
3
5 4
76
11
Unit Circle – Radian Measure
Degrees
Converting Degrees ↔ Radians
Recall oo
180,180
Converts degrees to Radians
o180Converts Radians to degrees
36
5
180
25
18025
oo
oo
50180
18
5
more examples
4
54
3
Coterminal angles – angles with a common terminal ray
Initial Ray
Terminal Ray
4
54
3
Coterminal angles – angles with a common terminal ray
Initial Ray
Terminal Ray
4
13
Trigonometric Ratios
θReference Angle
Adjacent Leg
HypotenuseOpposite Leg
hypotenuse
legoppositesin
hypotenuse
legadjacentcos
legadjacent
legoppositetan
Basic ratio definitions
2,0
Circle Trigonometry Definitions
(x, y)
Radius = r
Adjacent Leg = x
Opposite Leg = y
r
ysin
r
xcos
x
ytan
reciprocal functions
2,0
Unit - Circle Trigonometry Definitions
(x, y)
Radius = 1
Adjacent Leg = x
Opposite Leg = y
yy
1
sin
xx
1
cos
x
ytan
1
2
1,
2
3
6
2
3,2
1
3
2
2
3,
2
1
3
2
2
1,
2
3
6
5
2,0
2
1,
2
3
6
7
2
3,
2
1
3
4
2
3
2
3,2
1
3
5
2
1,
2
3
6
11
Unit Circle – Trig Ratios sin cos tan
6
4
3
(+, +)
(-, -)
(-, +)
(+, -)
2
1
2
1
2
3
3
3
32
3
2
3
2
11
6
3
2
1
12
3
Reference AnglesSkip π/4’s
2
2,
2
2
4
2
2,0
2
3
2
2
2
2
1
Unit Circle – Trig Ratios sin cos tan
6
4
3
2
2
2
2 1
2
2,
2
2
4
3
2
2,
2
2
4
5
2
2,
2
2
4
7
(+, +)
(-, -)
(-, +)
(+, -)
2
2,0
2
3
Unit Circle – Trig Ratios sin cos tan
6
4
3
(+, +)
(-, -)
(-, +)
(+, -)
sin cos tan
2
2
3 -1
1
1
-1
0
0
0
0
0
0
Ø
Ø
(0, -1)
(0 , 1)
(1, 0)(-1, 0)
0 /2π
Quadrant Angles
View π/4’s
6
4
3
2
3
2
4
3
6
5
2,0
6
7
4
5
3
4
2
3
3
5 4
76
11
Unit Circle – Radian Measure
sin cos tan
6
4
3
2
1
2
1
2
3
3
3
32
3
2
2
2
2 1
(+, +)
(-, -)
(-, +)
(+, -)Degrees
1sin cos tan
2
2
3 -1
1
1
-1
0
0
0
0
0
0
Ø
Ø
0 /2π
Quadrant Angles
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 θ in the standard position:
