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Algebra III Academic
Trigonometry
Angles in Degrees and Radians, Coterminal Angles and Reference Angles (Day 3)
Warm-Up
Solve the following using trigonometry.
1. The angle of elevation to the top of the Empire State Building in New York is 11o from a point on the
ground 1 mile from the base of the building. Find the height of the Empire State Building in feet.
2. A plane is flying at an elevation of 35, 000 feet within sight of the Gateway Arch in St. Louis, Missouri.
The pilot would like to estimate her distance from the Arch. She finds that the angle of depression to a point
on the ground below the arch is 22o .
a. What is the distance between the plane and the arch?
b. What is the distance between a point on the ground directly below the plane and the arch?
(along the ground)
3. From the top of a 200 foot lighthouse, the angle of depression to a ship on the ocean is 23o . How far is the
ship from the base of the lighthouse?
4. A 96 foot tree casts a shadow that is 120 feet long. What is the angle of elevation of the sun?
5. A man is lying on the beach, flying a kite. He holds the end of the kite string at ground level and estimates
the angle of elevation of the kite to be 50o . If the string is 450 feet long, how high is the kite above the
ground?
Algebra III Academic
Trigonometry: Angles and Degree Measure (Day 3)
Objective:
To use degrees to measure angles and become familiar with the unit circle.
Calculate coterminal angles and reference angles.
Write angles in different forms.
Where is trigonometry used?
 Astronomy, navigation, architecture, surveying…the list goes on and on.
Trigonometry: _______________________________________________________
If OA is rotated counterclockwise about O, we say that < BOA is an angle of rotation generated by OA. OB is
called the initial side and OA is called the terminal side.
Positive Angle:
*Rotate Counter-clockwise!
Negative Angle:
*Rotate Clockwise!
Draw the following.
1) Positive acute angle terminating in quadrant I.
2) Positive angle terminating in quadrant III.
3) Positive angle terminating in quadrant IV.
1)
2)
3)
Draw the following.
4) Negative acute angle terminating in quadrant IV.
5) Negative angle terminating in quadrant III.
6) Negative angle terminating in quadrant I.
4)
5)
6)
Coterminal Angles: _________________________________________________________________________
How to find coterminal angles…
q c = q g ± 360°
+
q c = q g ± 360°
-
(
)
Negative Coterminal Angle q c- < 0°
Positive Coterminal Angle (qc+ > 0°)
Ex.
Ex.
For the problems that follow, sketch the given angle  in standard position. Then, find one positive and one
negative coterminal angle. In which quadrant does the terminal side of the angle land?
  700
qc+ ( positive) = _____
3)   960
qc+ ( positive) = _____
qc (negative) = _____
qc (negative) = _____
qc (negative) = _____
Quadrant: _____
Quadrant: _____
Quadrant: _____
  50
qc+ ( positive) = _____
1)
-
  400
4)
2)
-
5)   625
-
6)   1234
qc ( positive) = _____
qc ( positive) = _____
qc ( positive) = _____
qc (negative) = _____
qc (negative) = _____
qc (negative) = _____
+
-
Quadrant: _____
+
-
Quadrant: _____
+
-
Quadrant: ____
Algebra III Academic
Trigonometry: Angles and Degree Measure (Day 3)
Homework
For the problems that follow, sketch the given angle  in standard position. Label  on your drawing.
Calculate a positive and negative coterminal angle  c . Determine the quadrant where the terminal side of your
angle lies.
1)
q = 50°
2)
3)   365
qc ( positive) = _____
qc ( positive) = _____
qc ( positive) = _____
qc (negative) = _____
qc (negative) = _____
qc (negative) = _____
Quadrant: _____
Quadrant: _____
Quadrant: _____
+
+
-
4)
  70
q = -400°
-
5)
q = -625°
+
-
6)   234
qc = _____
qc = _____
qc = _____
qc (negative) = _____
qc (negative) = _____
qc (negative) = _____
Quadrant: _____
Quadrant: _____
Quadrant: _____
+
-
+
-
+
-
Sketch the following angles. (Finding the coterminal angles may be helpful to determine the quadrant for the
angle that should be graphed).
a.  = 57°
b.  = 77°
c.  = 133°
d.  = 254°
e.  = -227°
f.  = -184°
g.  = 4897°
h.  = 220°
i.  = 302°