Trigonometry Worksheet Page 3
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22direction), and –630°, –990° and –1350° (one, two and three complete extra revolutions in the negative
direction). In practice, we usually choose the smallest measure in most applications (See Fig 5).
Fig 5
Example 2: Assume two rays meet, forming an angle of 27°. State this angle’s (a) supplement, (b)
complement, (c) coterminal in the opposite direction, and (d) coterminal with one extra revolution in the
positive direction.
Solution:
a) Its supplement is 180° − 27° = 153°.
b) Its complement is 90° − 27° = 63°.
c) Its coterminal measure would be 360° − 27° = 323°, but since it is traced in the opposite
direction, it would have a negative value. Therefore, its coterminal measure in the opposite
direction is −323°.
d) Its coterminal measure with one extra revolution in the positive direction is 27° + 360° =
387°.
Example 3: A screw is turned 6 complete rotations, plus another half rotation, before it is set tight.
What would be the angle through which this screw was turned?
Solution: Six complete rotations would give an angle of 6 × 360 = 2,160°, and the extra half-rotation
would be an extra 180°. Thus, the screw was turned a total of 2,340°.
Example 4: Determine the following angles:
1. Two angles are supplementary, with the second angle being twice as large as the first angle.
2. Two angles are complementary, with the second angle being one less than three times the
smaller angle.
Solution:
be the smaller angle’s measure. Therefore, the larger angle has a measure of 2 . Since they
1. Let
are supplementary, their sum is 180°. We solve for :
+ 2 = 180
3 = 180
= 60
The smaller angle is 60° and the larger angle is 120°.
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