Download Review-Trig-Mid-Term

REVIEW : MID TERM EXAM
TRIGONOMETRY/TOPICS
NAME : _________________________
I Basic Concepts
Multiple Choice
1. The smallest positive measure for an angle coterminal with 5000 is
a) 8600
b) -2160
c) 1400
d) 600
0
2) An angle of -150 is coterminal with an angle of
a) 2100
b) -5100
c) both a and b d) none
3) 1 + cot2θ = ?
a) 1
b) tan2 θ
c) sec2 θ
d) csc2 θ
4) cot 13.50 is
a)0.240
b) 4.165
c) -0.240
d)-4.165
5) The distance between A(-3, 0) and B(5, 1) is
a) 5
b) 65
c) 41
d) 29
2
6) sin θ csc θ cos θ is
a) cot θ
b) tan θ
c) sec θ
d) csc θ
0
0
0
7) The sum of (76 0’ 55”) and (65 65’ 10”) is 141 6’ 5”
a) True
b0 False
8) . To what angle would you refer to find sin 2400
a) 300
b) 600
c) 900
9) The reference angle of 235 0 is
a) 1250
b) 415 0
c) 55 0
10) cot  sec  cos  is equal to
a) sin 
b) cot 
c) 1
11) (3, 4, 6) is a Pythagorean Triple
a) True
b) False
0
12) The equivalent of 240 in radian measure is
a) 3/5
b) 5/3
c) 4/3
13) The equivalent of -11/6 in degree measure is
a) –210
b)- 330
c) –225
0
0
0
0
14) cos( 240 ) cos(60 )  sin( 240 ) sin( 60 ) is
a) ½
b) -1/2
c) 1
d) -1
15) 2250 is in what quadrant
a) II
b) III
c) IV
d) 45
d) sec 
d) 0
d) /15
d) –240
d) I
II Given the vertices of a triangle : (4, 5), (-3, 2), (0, -4)
a) draw the triangle
b) find the length of each sides of the triangle
c) find the perimeter
d) determine if the points are vertices of a right triangle
III Evaluate the six trigonometric functions whose terminal side lies in the following
points..= Sketch the triangle formed.
a) (-3, 4)
b) (-5, -2)
IV Find the six trigonometric function of
a) 5π/3
b) -3π/4
c) 300 0
V Using Trigonometric Identities, find the remaining functions of the following
3
a) cos   
b) sec  2
2
VI Find all the possible values  in the interval 0 0    360 0
2 3
1
a) sin   
b) tan   3
c) sec   
2
3
0
VII Find the missing parts of a right triangle (C = 90 ) given :
a) a = 10
A= 550
b) b = 13.5
c = 16.8
VIII Find the exact value of each part labeled with a variable in the given figure.
7
VIII Word Problems.
1. A scanner antenna is on top of the center of the house. The angle of elevation
from a point 28 meters from the center of the house to the top of the antenna is
270 10’, and the angle of elevation to the bottom of the antenna is 180 10’. Find
the height of the antenna.
2. A passenger in an airplane flying at 8000 ft over the ocean sights two towns. The
angles of depressions to the towns are 27 degrees and 39 degrees. Find the
distance between the two towns.
3. A 40 ft rope is stretched from the top of a 30 ft pole to the ground. What is the
angle of elevation of the rope?
4. Points A and B are on the west-east line and 20 miles apart. Point A detects a
plane at C on a bearing of 58020’. Point B simultaneously detects the same plane
on a bearing of 328020’. Find the distance from B to C.
VI Complete the chart
GRAPH
SET-BUILDER
INTERVAL NOTATION
[-5, 5)
{x / 5 ≤ x < -2}
RECIPROCAL IDENTITIES
PYTHAGOREAN IDENTITIES
sin   1 / csc 
csc   1 / sin 
sin 2   cos 2   1
cos   1 / sec 
sec   1 / cos 
1  tan 2   sec 2 
tan   1 / cot 
cot   1 / tan 
1  cot 2   csc 2 
QUOTIENT IDENTITIES
sin 
cos 
cos 
cot  
sin 
tan  
I
30
60
45
II
150
120
135
III
210
240
225
IV
330
300
315