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Chapter 7: Trigonometric
Functions
Section 7.1: Measurement of
Angles
Recall:
An angle is formed by two rays sharing a
common endpoint.
The initial ray is where the angle measure
begins.
The terminal ray is where the angle measure
ends.
Types of Angles
Positive angle – counterclockwise rotation
from the initial ray.
Negative angle – clockwise rotation from the
initial ray.
Common Angle Measures
Fill in as many angle measures as you recall
from Geometry:
Acute:
Obtuse:
Right:
Straight:
Reflex:
Reflex Angles
A Reflex Angle is one which is more than
180° but less than 360°
Units of Angle Measure
Degree – common unit for smaller angles.
Revolution – common unit for larger angles.
Radian – the number of radius units in the
arc length of the angle.
Conversions
Degrees to radians use:
Degrees ∙

180
Radians to degrees use:
Radians ∙
180

Example 1:
Covert the following degree measures into
radian measures:
1) 96º
2) 27º
3) 21º
4) 49º
Example 2:
Convert the following radian measures to
degree measures:
1) 7π
2) 6
5
3) 2π
4) 4
3
Central Angle
To find the measure of a central angle, θ, use
the following formula:
s
θ=
r
where s is the arc length and r is the radius of
the circle.
Example 7:
Using the formula, find the measure of the
central angle, θ, if the radius is 8 and the
arc length is 6.
HOMEWORK (Day 1)
pg. 261; 2 – 10 even (parts a and b only)
Standard Position
An angle is in standard position when it is
shown on the coordinate plane with its
vertex at the origin and the initial ray along
the positive x-axis.
Other Special Angles
Quadrantal angle – an angle where the terminal
ray in standard position lies along an axis.
The quadrantal angles are 0°, 90°, 180°,
270°, 360°, 450°, etc. and – 90°, – 180°,
– 270°, – 360°, etc.
Coterminal angles – two angles (angles with
the initial side on the positive x-axis) that
have the same terminal ray when they are
in standard position.
Coterminal Angles
To find a positive coterminal angle, add 360º
or 2π.
Ex. 3: Find a positive coterminal angle of 74º.
434°
Ex.4: Find a positive coterminal angle of
10
3
4
3
.
Coterminal Angles
To find a negative coterminal angle, subtract
360º or 2π until a negative angle is found.
Ex. 5: Find a negative coterminal angle of 390º.
-330°
Ex. 6: Find a negative coterminal angle of π.
-π
HOMEWORK (Day 2)
pg. 262; 18 – 20 all