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Problem Set 1

This document provides a problem set on preliminary trigonometry concepts including: the coordinate system and distance formula, angles and angular measures, triangles, the circle including arcs and central angles, and arcs, sectors, and segments of circles. Students are asked to find distances, plot points, determine quadrants, convert between degree/minute/second and radian measures, identify possible triangle side lengths, find missing angles of triangles, determine arc quadrants, and calculate arc lengths.

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eugenio
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622 views6 pages

Problem Set 1

This document provides a problem set on preliminary trigonometry concepts including: the coordinate system and distance formula, angles and angular measures, triangles, the circle including arcs and central angles, and arcs, sectors, and segments of circles. Students are asked to find distances, plot points, determine quadrants, convert between degree/minute/second and radian measures, identify possible triangle side lengths, find missing angles of triangles, determine arc quadrants, and calculate arc lengths.

Uploaded by

eugenio
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Problem Set 1: Preliminary Concepts

Math 513 - Modern & Plane Trigonometry

EUGENIO E. BALASABAS
MATH 513

I. The Coordinate System and Distance Formula


1. Find the directed and undirected distances from
a. -5 to 19
ANSWER: The directed distance 5 and 19
Undirected distance is 24
b. 46 to -18
Answer: The directed distance 18 and 46
Undirected distance is 64

2. Plot each given pair of points in the plane and find the distance between them.
a. (-3 , 2) and (5 , 3)

b. (-1 , 3) and (2 , 5)
II. Angles and Angular Measures
1. Determine the quadrant where the terminal side of each of the following angles lies:
a. 5930 Answer: QUADRANT III
b. b. -1570 Answer: : QUADRANT III
2. Find two angles coterminal with
a. 4590

b. -2370

3. Convert the following to degrees and minutes:


a. 49.640

b. b. 78.350

4. Convert the following to degree measures:


a. 350 30’

b. b. 740 8’ 24”
III. Triangles
1. Which of the following sets of measures could be lengths of the sides of a triangle?
a. { 4 , 9 , 13 } b. { 5 , 8 , 10 } c. { 2 , 2 , 4 }

2. Which of the following sets of measures could be lengths of the sides of a right triangle?
b. { 3 , 4 , 6 } b. { 5 , 12 , 13 } c. { 6 , 9 , 11 }
3. Find the measure of the third angle of the triangle given the measures of its two other angles:
a. 390 , 650

b. 140 12’ , 930 48’

c. 1230 15’ 32” , 160 12’ 47”


IV. The Circle: Its Arcs and Central Angle
1. Determine the quadrant where each arc having the following given length would terminate:
a. s = 12 QUARTER 4
b. -18.46 QUARTER 1
c. s = 39.75 QUARTER 3

2. Change to radians (Use 10 = 0.01745)


a. 4500 =7.85 Rad
b. -3450 = -6.0rad2
c. 293.70 =5.125 rad
3. Change to degrees (Use 1 rad = 57.30)
a. 34 rad =1948.2 degrees
b. 0.9 rad =51.57 degrees
c. 14 π =2520 degrees

V. Arc, Sector and Segment of a Circle


1. Find the arc length cut by a circle with the given radius r and θ.
a. r = 4 cm , θ = π/2 rad

b. r = 18.11 cm , θ = 1350

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