Honors Pre-Cal
Name
Things you need to recall from Algebra 2 to get started with
Trigonometry in Pre-Cal
Use – Pre-Cal Textbook Chapter 4 as a reference
Just like there are different units for measuring length, such as inches and centimeters, and
different units for measuring weight, such as kilograms and pounds, there are different units for measuring
angles.
The unit that you have been using for angle measurement is the degree. The Babylonians were
probably the first people to use the degree as a unit of measurement after they decided to divide a circle
into 360 equal parts. Therefore, a circle is 360.Another unit of measurement for an angle is the radian.
The radian unit was created using the circumference of a circle that has a radius of 1 (called a unit circle).
Since the formula for circumference is C = 2r, there are 2 radians in a unit circle. Therefore, a circle is
also 2R. Notice that you can use a little “R” to denote radian measurement; it is NOT an exponent.
Since we know that a circle has 360 degrees and it also has 2 radians, we can use this relationship to change
angle measurements from degrees to radians or radians to degrees. We can reduce further to 180 degrees is
equal to 𝜋 radians.
Example #1: Change 65 to radians.
Set up (
Multiply
𝜋
180
Example #2: Change
) ∙ 65 =x
𝑥=
Set up (
65𝜋
180
Divide & reduce
So, 65 is equal to
Multiply
𝑥=
13𝜋
36
180 𝜋
𝜋 ) ∙ 12 = 𝑥
180𝜋
12𝜋
=𝑥
13𝜋
36
Divide & reduce
.
Honors Pre-Cal Notes – Trigonometry

to degrees.
12
So,
page 1/4
𝑥 = 15

is equal to 15.
12
Find the exact number of radians for each degree measure. Leave your answers in reduced, fraction form.
1.
60°
2. 150°
3. 95°
4.
80°
Find the exact number of degrees for each radian measure.
5.

8
6.
3
2
7.
3𝜋
5
In Algebra, “x” and “y” are the most commonly used variables. In Trigonometry, Greek letters are often
used to represent angles or angle measurements. Some commonly used Greek letters and their names are
listed below.

alpha

beta

gamma

theta

phi

omega
Theta, , is the most common in trigonometry.
Circular Arc Length
Recall from Geometry that arc length of a circle is a fraction of its circumference. Therefore, if θ is a
central angle in a circle of radius r, and θ is measured in radians, then the length, s, of the intercepted arc is
𝑠 = 𝑟𝜃.
If θ is measured in degrees, then the length, s, of the intercepted arc is
𝑠=
𝜋𝑟𝜃
180
.
Find the missing information.
s
8
9.
10.
11.
r
θ
2 in
25 radians
_________
π/4 radians
5 ft
18°
1m
_________°
_________
1.5 ft
_________
3m
Honors Pre-Cal Notes – Trigonometry
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Reference and Coterminal Angles
In Pre-calculus, when you graph an angle you will usually draw the angle in standard position. This means you
will put the angle on an x-y graph; the vertex of the angle is at the origin (0, 0) and one side of the angle
(called the initial ray) will be on the positive x-axis. The other side of the angle (called the terminal ray)
can be anywhere else.
Terminal Ray
135 angle of rotation
Initial ray
The degree measure of the angle indicates the amount of rotation from the initial ray to the terminal ray; if
you rotate counter-clockwise the degree measure is positive and if you rotate clockwise the degree measure
is negative.
Examples:
Directions: Sketch the angles below in standard position; use an arrow to show the direction of rotation.
For each angle, state the quadrant (I, II, III, or IV) in which the angle
terminates.
12.
16.
190
28
13.
-45
14.
123
17.
287
18.
-200
15. 480
19.
-164
It is possible for angles with different degree measures to terminate at the same place. For example, 493
terminates at the same place as 133 after going through one more complete revolution. -227 also
terminates at the same place as 133 by rotating clockwise
instead of counterclockwise.
Two angles in standard position are coterminal if they terminate at the same place.
So 133, 493, and -227 are coterminal angles.
Honors Pre-Cal Notes – Trigonometry
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Directions: For each angle below, state two coterminal angles.
20.
73
21.
-46
22.
205
23.
317
24.
-192
25.
90
26.
-115
27.
23
The reference angle of an angle in standard position is the positive, acute angle (or right angle) between the
x-axis and the terminal side of the angle.
in Quadrant I:
 = 71
ref = 71
in Quadrant II:
 = 133
ref = 47
in Quadrant III:
 = 254
ref = 74
in Quadrant IV:
 = 317
ref = 43
Directions: For each angle below, draw the angle in standard position, find the measure of the
reference angle, and mark the reference angle on your sketch.
28.
137
29.
198
30.
259
31.
147
32.
-160
33.
21
34.
-220
35.
-86
Honors Pre-Cal Notes – Trigonometry
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