Similar Triangles, Right Triangles, And The Definition Of The Sine, Cosine And Tangent Functions Of Angles Of A Right Triangle Worksheets With Answer Key Page 2
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43Since one counterclockwise revolution forms an angle of 360° or 2π radians, the equations for
converting between degrees and radians are
π
π
2
°
=
radians =
radians
1
360
180
and
360
180
1 radian =
degrees =
degrees.
π
π
2
Problems:
3. What is the radian measure of 108° angle?
π
7
4. What is the degree measure of an angle of
radians?
18
π
5
−
5. What is the degree measure of an angle of
radians to the nearest tenth of a degree?
17
ARC LENGTH
If an arc of length s on a circle of radius r subtends a central angle of radian measure θ, then
s = rθ.
Example: Consider a circle with radius 4.
What is the arc length intercepted by a 45° angle?
π
°
=
Solution: First convert to radians:
45
.
4
π
θ
=
And so with
we have
4
θ
=
s
r
π
π
=
=
Figure T4
s
4
.
4
Problems:
6. Determine the arc length intercepted by a 78° angle in a circle of radius 3.5.
π
9
7. Determine the arc length intercepted by
radians in a circle of radius 4.
5
AREA OF A SECTOR
Consider the sector determined by the angle θ, in
the circle with radius, r. The arc length of a 180° is π.
π
=
2
A
r
Recall that the area of the circle is given by
.
θ
Since the sector is the fractional part
of the circle,
π
2
the area of the sector then is given by
θ
θ
2
r
π
=
⋅
=
2
A
r
.
Figure T5
π
2
2
- 2 -
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education