Trigonometry
ANGLES OF ROTATION –
SECTION 1.1 DAY 2
Getting ready for class
 What is meant by standard position for an
angle?
 Given any angle, how do you find another
angle that is coterminal to it?
 One complete revolution is ____ degrees.
Solve the following problems and write
the answers on a piece of paper.
 1. It takes the earth 24 hours to make one
complete revolution on its axis. Through how
many degrees does the earth turn in 12 hours? In
one hour?
 2. A turntable in a shop makes 45 revolutions per
minute. How many revolutions does it make per
second?
 3. A tire is rotating 15 rpm (revolutions per
minute). How many degrees does it turn in 5
seconds?
Angles of Rotation
 If two angles have a sum of 90⁰, then they are
called complementary angles and we say
each is the complement of the other.
 Two angles with a sum of 180⁰, are called
supplementary angles and we say they are
supplements of each other.
Find the complement and the
supplement of each angle.
1. 40⁰
2. 110⁰
3. 240⁰
4. Θ
Answers
1. complement 50⁰
supplement 140⁰
2. C = -20⁰
S = 70⁰
3. C = - 150⁰
S = -60⁰
4. Complement 90⁰ – θ
Supplement 180⁰– θ
Find the measure of each marked
angle
Fractional parts of degrees
 With calculators it is convenient to use
decimal degrees to denote fractional parts of
degrees.
 Historically, however, fractional parts of
degrees were expressed in minutes and
seconds, using the prime ( ' ) and double
prime( '' ) notations, respectively.
 Phrases like “minutes” and “seconds”
are used to make a connection between
time and the fraction of a degree that is
associated with these phrases.
 1' = one minute = (1/60)(1°)
 1'' = one second = (1/60)(1') or
(1/3600)(1°)
Convert 64°32'4'' to decimal
degree
 Every calculator has a different set of
procedures for this task…hopefully you will
use the same calculator all semester.
 Some scientific calculators have a button that
says DMS → DD
 In that case, you enter the value as 64.3204
(even though it is not a decimal) then hit the
DMS → DD button.
 64.5344
Convert 64°32'4'' to decimal
degree
 On a graphing calculator,
 ANGLE (option 1 is degree °)
(option 2 is minute ')
ALPHA (+) is ''
 ENTER
 64. 5344
Additional Examples:
 Convert 120.6° to DMS
 On a scientific calculator use the
DD→ DMS button.
 On a graphing calculator, go under the
ANGLE menu (option 4)
 120° 36'
Convert -34.36° to DMS
 -34° 21' 36''
Additional problems:
 Find the complement and supplement of
20° 10' 30"
 Find one positive and one negative
coterminal angle to 150° 40' 35"