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Review from 13-1
1. Assume C represents the right angle and c is the
o
hypotenuse. If A= 50 and a= 11 find all the other angles
and sides. Round angles to degrees. Sides to tenths.
B= 40 degrees
b= 9.2, c= 14.4
2. The top of a staircase is 3.5 meters higher than the
bottom. Viewed from the side, the horizontal length is
4.75 meters. Find the angle of depression from the top
of the stairway to the bottom
36.4 degrees
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Alg. II
April 08, 2008
13-2 Angles and Angle Measures
An angle in standard position is an angle that has its vertex at the origin, and one ray,
called the initial ray, along the positive x-axis. The second ray of the angle is called the
terminal side. If you think of the terminal
side starting from the same position as the initial ray and rotating counterclockwise about
O to its final position, the angle generated
is positive. Angles in standard position that have the same terminal side are called
coterminal angles.
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Draw the following angles in standard form. Are any of these
coterminal angles?
a. 150 degrees
b. -210 degrees
y
y
x
x
c. 120 degrees
d. 480 degrees
y
x
y
x
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Degrees are commonly used in applications involving surveying and
navigation. However, in the late 1800’s mathematicians began to see the
need for another unit of measure, called a radian, that would simplify
certain mathematical and physical formulas.
The definition of a radian is based on the concept of a unit
circle, which is a circle of radius 1 unit with its center at
the origin of a coordinate system. The radian measures are
based on the length of an arc on the unit circle. In the
figure at the right, q is in standard position so that the
rays of the angle intercept an arc with length of 1 unit.
The measure of this angle is defined to be 1 radian.
q
The circumference of any circle is 2pr, where r is the radius measure. So
the circumference of a unit circle is 2p(1) or 2p units. Therefore, the angle
representing one complete revolution of the circle measures 2p radians.
180 degrees would be ________ radians.
90 degrees would be _______radians
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16. 3 radians
17. -1 ¼ radians