CW#61H: Angles and Radian Measure
Honors Geometry
Teacher Notes – KEY
CRS
FUN 703 - Exhibit knowledge of unit circle trigonometry
Objective



10.6 - Draw positive and negative angles on a coordinate system
10.7 - Define and apply definition of coterminal angles
10.9 - Convert angle measures between degrees to radians
REVIEW! (Radians – a NEW way to measure angles!) Drawing Angles in the Coordinate Plane
[explain: In a coordinate plane, an angle can be
formed by fixing one ray, called the initial side, and
rotating the other ray, called the terminal side,
about the vertex.
Investigate: What a radian means using a circle of
radius 6..
How many radians are there in a circle?
What is the full distance around a circle?
Notice: arc length = the circumference is 2π × 6. And remember:
So in radians, the angle right around this circle is:
central angle >> the vertex is at the center of
the circle.
Therefore, there are 2 radians in a full circle.
Radian = subtended central angle of a circle
formed by an arc whose length equals the
radius, alternative way of measuring angles, or the
amount of turn.
NEW STUFF: Label the coordinate plane in terms of radians (Tell me the
degree conversion for each)
Subtend = “opposite” or “appears to occupy” or
“extend underneath” (ARMS subtend desk, desk
subtends you example)
The angle subtends the arc
The arc subtends the angle
Wait, so is it possible to have negative angle measures? Counterclockwise
movement = positive
Clockwise movement = negative
Ex - What angle does the hypotenuse of a right
triangle subtend? [ans: right angle]

Ex. 1) Draw an angle of 100° and label the axes (In notebooks)
Ex. 2) Draw an angle of -280° and label the axes.
Ex 3) Draw an angle of -30° and label the axes. Now draw an angle of -390°.
What do you notice about the angles?
An angle is in “standard position” if its vertex is at the origin and its initial
side lies on the positive x-axis.
Co-terminal angles: terminate or “land” in the same spot, but
To find coterminal angle, you must add 360 or subtract
have different notations
multiples of 360. Coterminal angles can be
POSITIVE or NEGATIVE.
Example 4) Find one positive and one negative coterminal
Example 5) Find one positive and one negative coterminal
angle of -134°
angle of 395°
[ans: positive coterminal = -134° + 360° = 226°
[ans: positive coterminal = 395° - 360° = 35°
negative coterminal = -134° - 360° = -494° ]
-or- 395° + 360° = 755° negative coterminal = 395° - 2(360)°
= -325° ]
PUSH IT TO THE LIMIT.
CW#61H: Angles and Radian Measure
Honors Geometry
CLASSROOM COPY – DO NOT WRITE ON!!!
CRS
FUN 703 - Exhibit knowledge of unit circle trigonometry
Objective



10.6 - Draw positive and negative angles on a coordinate system
10.7 - Define and apply definition of coterminal angles
10.9 - Convert angle measures between degrees to radians
1) Draw a 135° angle.
2) Draw a -400° angle.
a. Find one positive angle that is coterminal with
the given angle.
a. Find one positive angle that is coterminal with
the given angle.
b. Find one negative angle that is coterminal with
the given angle.
b. Find one negative angle that is coterminal with
the given angle.
3) Name 3 positive coterminal angles of
terms of radians.
4) Name 3 positive coterminal angles of 0 in
terms of radians.
in
0
Name 3 negative coterminal angles of
of radians.
in terms
Name 3 negative coterminal angles of 0 in terms
of radians.
What is in degrees? (Use the picture above.)
What is in degrees? (Use the picture above.)
5) Directions: Use a protractor to measure each angle in degree in the graph below. Then convert each
degree measure to radians. The first two angles have been done for you. Do you notice any patterns?!
PUSH IT TO THE LIMIT.
Practice Quiz Questions (Mixed Review):
6) The angle of repose is the steepest angle at which
dry, unconsolidated sediment is stable. You create a
conical pile of sand that is as steep as you can make it.
The pile is 11 cm high and has a radius of 16 cm.
What is the angle of repose of this sand?
7) Given the approximation Cos 21° 0.93, use
trigonometric identities to find the approximate
value of:
a) Sin 21°
b) Tan 21°
c) Cos 69°
d) Sin 69°
e) Tan 69°
8) If tan = 4, find the value of :
tan + tan( – )
9) If sin = 0.3, find the exact value of :
sin + cos( – )
*Hint: use trig inverses to find *
10) A 6’3” basketball player stands at the foul line for
a free throw. The distance from the free throw line to
the point on the floor below the basket is 14’. If the
height of the basket is 10’, find the angle of elevation
from the player’s line of sight to the basket. Draw a
picture to help you.
12) The distance from the origin to the point (x,y) in
the 1st quadrant is 22. If the angle formed by the x-axis
and the line that passes through the origin and point
(x,y) is 28°, find the point (x,y).
11) Solve for
13) Combining Forces Juana and Diego Gonzales,
ages six and four respectively, own a strong and
stubborn puppy named Corporal. It is so hard to take
Corporal for a walk that they devise a scheme to use
two leashes. If Juana and Diego pull with forces of 23
lb. and 27 lb. at the angles shown in the figure, how
hard is Corporal pulling if the puppy holds the
children at a standstill?
PUSH IT TO THE LIMIT.