Graphs of Trigonometric
Functions
Angles and Radian Measure

180
• 1 radian = degrees
• 1 degree =
π
180 radians

1.
π
Solution:
2.
−
7
8
π
Solution: −
7 π
8
= −
7 π x
=
8
− 157.5
o
180 o
π
115 o =
115 o x
π
180 o
=
23 π
36

Equivalent Values
120 o =
2
π
3
150 o
135 o =
3
π
4
=
5
π
6
180 o = π
210 o =
7
π
6
225 o =
5
π
4
240 o =
4
π
3
90 o =
π
2
270 o =
3
π
2
60 o =
π
3
45 o =
π
4
30 o =
π
6
0 o =
⎨
360 o
0 radians
=
2
π
300 o
330 o
315 o =
7
=
11
π
π
6
4
=
5
π
3

• When determining the value of a trigonometric function, you can use the unit circle and reference angle. Remember once you locate the reference angle, watch the signs of each of the six trigonometric functions. These signs depend on the quadrant in which the reference angle lies.

Example # 1
• Evaluate tan
25
π
6
• Solution: The reference angle for
25 π
6 is
π
6 which is 30 o
⎛
⎜⎜
The terminal side of the angle intersects the unit circle at a point with coordinates
2
3
,
1
2
⎞
⎟⎟
6
π tan
25
6 positive.
= tan30 o
1
=
1
=
2 3
3
2 =
3
3

• Radian measure can also be used to find the length of a circular arc. A circular arc is a part of a circle. The arc is often defined by the central angle that intercepts it. A central angle of a circle is an angle whose vertex lies at the center of the circle.
Central angle
Circular Arc

•
• The length of any circular arc s is equal to the product of the measure of the radius of the circle r and the radian measure of the central angle θ that it subtends.
S = r θ

• Given a central angle of 125 degrees, find the length of its intercepted arc in a circle with radius 7 centimeters. Round to the nearest tenth.
• Solution: First convert the measure of the central angle from degrees to radians. 125 o
= 125 o x
π
180 o
=
25 π
36
• Then find the length of the arc. s = 7x
25 π
36
≈ 15.3cm

• A sector of a circle is a region bounded by a central angle and the intercepted arc.

expressed in radians and r is the measure of the radius of the circle, then the area of the sector, A, is as follows.
A
=
1
2 r
2

• Find the area of a sector if the central angle measures radians and the radius of the
7 circle is 11 centimeters. Round to the nearest tenth.
1
2
3
π
A
=
( 11 )
2 7
=
81 .
5 cm
2

• Section 6-1
• Pp. 348-351
• #16-33 all, 35, 37, 38, 43, 45, 46,
• 60, 63, 65