1. No category

PC CHAP 5 SEC 1 HOMEWORK:
For questions 1, 6, 11, find the measure (if possible) of the COMPLEMENT and
SUPPLEMENT of each angle.
1) 15o
(6) 19o 42’ 05” 19.70139o
75o, 165o
(11)
2𝜋
𝜋
,
3𝜋
5
10 5
For question 16, determine the measure of the positive angle with measure less than 360o
that is COTERMINAL with the given angle and then classify the angle by quadrant.
Assume the angles are in standard position.
16) α = -872o
208o it is in Quadrant III
For question 21 use a calculator to convert each decimal degree measure to its equivalent
DMS measure.
21) 18.96o
64o9’28.8”
For question 26 use a calculator to convert each DMS measure to its equivalent decimal
degree measure.
26) 63o 29’ 42”
63.495o
For questions 3, 36 and 41, convert the degree measure to exact radian measure.
31) 30o
𝜋
(36) 315o
6
7𝜋
4
(41) -9o
−𝜋
20
For questions 46 and 51, convert the radian measure to exact degree measure.
46) −
2𝜋
3
-120o
(51)
11𝜋
3
660o
For question 56, convert radian to degree or degree to radian. Round your answer to the
nearest hundredth.
56) -2.3
-131.784o
For question 61, find the measure in radians and degrees of the central angle of a circle
subtended by the given arc. Round approximate answers to the nearest hundredth.
61) r = 2 inches and s = 8 inches.
4 rad, 229.18o
For question 66, find the length of the arc that subtends the central angle with the given
measure in a circle with the given radius. Round your answer to the nearest hundredth.
66) r = 3 feet, and 𝜃
=
7𝜋
2
s=
21𝜋
2
feet = 32.97 feet
For question 69, find the number of radians in the revolution indicated.
69) 1 ½ revolutions. 3π
71) ANGULAR ROTATION of TWO PULLEYS: A pulley with a radius of 14 inches uses a
belt to drive a pulley with a radius of 28 inches. The 14-inch pulley turns through an angle of
150o. Find the angle through which the 28-inch pulley turns.
5𝜋
rad or 75o
12
76) ANGULAR SPEED: A wheel is rotating at 200 revolutions per minute. Find the angular
speed in radians per second.
20𝜋
3
91) NAUTICAL MILES and STATUTE MILES: A nautical mile is the length of an arc, on
Earth’s equator, that subtends a 1’ central angle. The equatorial radius of Earth is about 3960
statute miles.
a) Convert 1 nautical mile to statute miles. Round to the nearest hundredth of a statute mile.
1.14 statute miles
b) Determine what percent (to the nearest 1%) of Earth’s circumference is covered by a trip
from Los Angeles, California, to Honolulu, Hawaii (a distance of 2217 nautical miles).
10%
For question 96, find the area, to the nearest square unit, of the sector of a circle with the
given radius and central angle.
96) r = 30 feet, and Θ = 62o.
486.7 feet
BONUS: Latitude describes the position of a point on Earth’s surface in relation to the equator.
A point on the equator has a latitude of 0o. The North Pole has latitude of 90o. Determine how far
north, to the nearest 10 miles, the given city is from the equator. Use 3960 miles as the radius of
Earth.
The city of Miami has a latitude of 25o 47’ N.
1780 miles