Name _______________________________________________________________
Date _______________________________________
Trigonometry Notes
Section 1.1: Angles
Angle: formed by rotating a ray about its endpoint
Counter-clockwise = positive rotation
Clockwise = negative rotation
Angle Measures: most common units of measurement are degrees or radians
Degree Measure
1 complete rotation (or revolution) of a ray = 360°
Each degree contains 60 minutes
Each minute contains 60 seconds
We will use the Greek letter Ɵ (theta) as the name of the angle. Other letters will also be used throughout the text.
Right angle __________________
Acute angle ___________________
Obtuse angle ________________
Straight angle _________________
Complementary angles: two positive angles with a sum of __________.
Supplementary angles: two positive angles with a sum of ___________.
Ex. 1: Find the measure of each angle under the given condition.
a. angles with measures 6m° and 3m° are complementary
b. angles with measures 4k° and 6k° are supplementary
c. angles with measures 10m+7 and 7m+3 degrees are supplementary
Calculating with degrees, minutes, and seconds (DMS)
Ex. 2: Perform each calculation
a. 51°29’ + 32°46’
b. 90° - 73°12’
Most of the time we will use decimal degrees (DD), but you should be familiar with both and how to convert from
one to the other. Most calculators will perform the operation easily if you know how to use them.
Ex. 3: Converting between DD and DMS
a. Convert 74°8’14” to decimal degrees
b. Convert 34.817° to degrees, minutes, and seconds
DRAWING ANGLES IN STANDARD POSITION:
Standard Position of an Angle: vertex is at the origin, (0, 0). Initial side lies on the positive x-axis. An angle is said
to lie in the quadrant that contains its terminal side.
Example: Draw the angle 65˚
Example: Draw the angle 195˚
If the terminal side lies on one of the axes, it is called a quadrantal angle. Quadrantal angles are multiples of
___________.
Ex. Draw the following angles in standard position.
a) 450˚
Coterminal angles:
b) ˚-75˚
c) 285˚
angles with the same initial and terminal sides but different angle measures. The measures
of coterminal angles will differ by multiples of __________°.
To find coterminal angles, simply add or subtract multiples of 360˚.
Ex. 4: Finding measures of coterminal angles.
Find the angles of smallest possible positive measure coterminal with each angle.
a. 908°
b. -75°
The expression ______________________________ can be used to generate all angles coterminal with a given angle Ɵ,
where n represents any integer.
Ex. 5: Analyzing revolutions or rotations of an object. Keep in mind that 1 revolution (a turn around) is equal to
360˚.
a.
CAV (Constant Angular Velocity) DVD players always spin at the same speed. Suppose a CAV
player makes 480 revolutions per minute. Through how many degrees will a point on the
edge of a DVD move in 2 seconds?
b.
An airplane propeller rotates 1000 times per minute. Find the number of degrees that a
point on the edge of the propeller will rotate in 1 second.
Classwork (to be finished for homework): Pages 6-8 #1-4, 5-17 odd, 19-22, 23-57 odd (skip 43),
60, 61-67 odd, 75, 77