1.  sin
225°
2.  tan 270°
3.  sec 300°
-1
4.  tan (tan 3/5)
5.  cos (sin-1 -√3/2)
-1
√3
6.  tan ( /3)
Trigonometry
1
6.1
Algebra II
¡ 
¡ 
¡ 
The RADIAN measure of an angle in the unit
circle is the length of the corresponding arc…
it is a linear measure as opposed to an
angular measure.
A radian is defined as the angle between 2
radii (radiuses) of a circle where the arc
between them has length of one radius.
A radian is the angle subtended by an arc of
length r (the radius). Trigonometry
3
Trigonometry
4
For any circle, 2πr is the circumference. In a unit circle r = 1 so the circumference of
the unit circle is 2π. Therefore there are 2π radians in circle. There are 360° in a circle so 2π radians = 360°
π radians = 180°
1 radian = 180°
π
Trigonometry
5
There are 2π radii around the circumference
of a circle, or about 2 times 3.14 or 6.28
radii around the circumference of a circle. Each one of these radius lengths would
designate one radian, so there are about
6.28 radians in a full circle. One radian is approximately 57.3°. Trigonometry
6
2π ≈ 6.28 is the
circumference of
the unit circle 2π = 360°!!!
Trigonometry
7
¡ 
There is another unit for measuring angles, called
gradians. The right angle is divided into 100
gradians. Gradians are used by surveyors, but not
commonly used in mathematics. However, you will
see a “grad” mode on most calculators. Trigonometry
8
Trigonometry
9
1. 2.
π
3
3π
2
60°
5π
5. 6
150°
270°
6. 165.6°
2.89
3. 6.14 351.8°
π
4. 2
Trigonometry
90°
10
If π radians = 180°
Then…
π = 1°
180 Trigonometry
11
1. 45°
π
2. 60°
π
3. 150°
5π
6
4. 120°
2π
3
Trigonometry
5. 90°
6. 315°
7π
4
4
π
3
2
12
Trigonometry
13
Trigonometry
14
Trigonometry
15
Trigonometry
16
1.
2.
π
π
+ 2 π k, where k is an int
3
3
7π
−5π
3
3
3π
4
Trigonometry
3π
+ 2 π k, where k is an int
4
11π
−5π
4
4
17
1.
5π
6
π
6
2.
7π
4
π
4
3.
4π
3
π
3
Trigonometry
4.
7π
3
π
3
5.
15π
4
π
4
6.
8π
3
π
3
18
1.
5π
cos
4
2π
2. cot
3
11π
3. sin 6
Trigonometry
2
−
2
3
−
3
1
−
2
19
4.
−1
17π
5. sin
6
1
2
sec − 5π
11π
6. csc 4
Trigonometry
2
20
7.
19π
sec
6
2 3
−
3
25π
8. cot
4
1
π
9. tan −
3
Trigonometry
− 3
21
To find arc length: S= rθ
To find the area of a sector:
1 2
A= r θ
2
***θ must be in radians!!!*** Trigonometry
22
S= rθ
S= (6.8)(2.23)
S= 15.19 m
π
128° ×
= 2.23
180
1
2
A = (6.8) (2.23)
2
A = 51.6 m
Trigonometry
2
23
S= rθ
14.2= (r)(1.047)
S= 13.56 cm
π
60° ×
= 1.047
180
Trigonometry
24
S= rθ
10
S= ( )(3)
3
S= 10 m
1 2
15 = (3) (θ )
2
10
θ=
3
Trigonometry
10 180
×
=
3
π
190.98°
25
S= rθ
π
S= (1.4)( )
6
S= 0.73 m
π
30° ×
=
180
Trigonometry
π
6
26