Trigonometry Worksheet Page 4
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22be the smaller angle, the larger angle is 3 − 1, and their sum is 90°. We solve for :
2. Letting
+ { 3 − 1 { = 90
4 − 1 = 90
4 = 91
91
=
= 22.75
4
The smaller angle is 22.75° and the larger angle is 67.25°.
Comment: the Greek letter
(theta) is often used to represent an angle.
Radian Measurement
Suppose we overlay a circle with radius 1 on the xy-plane, its center at the origin. This is called the unit
= 2 { 1 { = 2 . A ray is drawn from the origin, intersecting the circle at
circle, and its circumference is
point P (see Fig. 6). This ray is the terminal side of an angle, with the initial side being the positive x-
axis, and this angle “cuts off” (subtends) a portion of the circle. The portion of the circle from (1,0) to
point P (in the positive direction) is called an arc of the unit circle, and its length will be proportional to
the circle’s circumference (which is 2 ) in the same way the angle’s measure will be to 360°:
Fig 6
length of arc {radian measure{
angle in degrees
=
2π
360°
The length of the arc is called the radian measure of the subtending angle.
A complete unit circle covers 360° and has a circumference of 2 . Therefore, we can relate these two
facts as follows:
360 degrees = 2 radians
Dividing both sides by 360 gives us
$
1 degree =
radians
=
# "
% "
# "
Or, we can divide by 2 , which gives us
# "
% "
# "
degrees = 1 radian.
=
$
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