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問題一覧
1
Sin A cos B - cos A sin B is equivalent to:
sin(A-B)
2
The angular distance of a point on the terrestrial sphere from the north pole is called
coaltitude
3
Csc 520° is equal to
csc 20°
4
What is the sine of 820°?
0.984
5
The logarithm of the negative number is
imaginary
6
The sum of the squares of the sine and cosine of an angle.
1
7
The logarithm of a number to the base e (2.7182... .) is called
Napierian logarithm
8
The characteristic is equal to the exponent of 10, when the number is written in
logarithmic form
9
Napierian logarithms have a base closest to which number?
2.72
10
The logarithm of 1 to any base is
zero
11
Sin (270° + β) is equal to
-cosβ
12
The sum of the angles in an octant spheric triangle is
270°
13
The median of a triangle is the line connecting the vertex and the midpoint of the opposite side. For a given triangle, these medians intersects at a point which is called the
centroid
14
The altitude of the sides of the triangle intersects at the point known as
orthocenter
15
The angle which the line of sight to the object makes with the horizontal which os above the eye of the observer is called
angle of elevation
16
Log M - log N id equal to
log(M/N)
17
The other form of loga(N) = b is
N=a^b
18
The point of concurrency of the altitude of the triangle.
orthocenter
19
The point of concurrency of the perpendicular bisector of the sides of the triangle.
circumcenter
20
The point of concurrency of the angle bisector of the triangle is called
incenter
21
The logarithm of the reciprocal of N is called the _______ of N.
cologarithm
22
The inverse function of a logarithm is known as
antilogarithm
23
The cologarithm of a number is the ______ of the logarithm of a number.
negative
24
The first table logarithms with 10 as base was developed in 1615 by
Henry Briggs
25
Who invented logarithms in 1614?
John Napier
26
The number loga(b) is called the ____ of the system of a base a with respect to the system of base b.
modulus
27
Napierian logarithm has a base of
e
28
Log x = _________ ln x.
0.434
29
lnx = ________ logx
2.303
30
Which of the following cannot be a base for a logarithm.
1
31
the integral part of a common logarithm is
characteristic
32
The mantissa of a logarithm is
positive value or zero
33
For 0 < x < 1, ln x is
negative
34
If < N < 10, then
1 < log N < 2
35
To change loga to logb N, multiply loga N by
logb(a)
36
The numbers loga(b) and logb(a) are
reciprocal to each other
37
Logarithm using 10 as base .
Common logarithm
38
The logarithm of a product is the _____ of the logarithms, and the logarithm of a quotient is the ________ of the logarithms.
sum, difference
39
When a logarithm is expressec as an integer plus a decimal (between 0 and 1), the integer is called
Characteristic
40
The characteristic of a logarithm is 3. The number between
1000 and 10000
41
Tha characteristics of the common logarithm of a number greater than 1 is
zero or positive
42
The characteristic is ____ the exponent of 10, when the number is written in scientific notation.
equal to
43
If logarithm to base 10 (denoted as log10) is called common logarithm is called natural logarithm, what do you call the logarithm of base 2 (denotes as lb)?
Binary Logarithm
44
If the unknown is a conditional equation occurs as an exponent, the best way to solve the unknown is by
taking the logarithm of both sides
45
Angles of rotation with the same initial side and terminal side.
Coterminal Angle
46
An angle equal to revolution of 360°
Perigon
47
The angle which the line of sight 'to the object makes with the horizontal is above the eye of an observer.
Angle of elevation
48
The angle which the line of sight to the object makes with the horizontal is below the eye of an observer.
Angle of depression
49
The triangle inscribed in a given triangle whose vertices are the feet of the three perpendiculars to the sides from some point inside, the given triangle.
Pedal Triangle
50
The right triangle whose length of sides may be expressed as ratio of integral units.
Primitive triangle
51
A triangle with no side equal is known as
Scalene triangle
52
If two triangles have congruent bases, then the ratio of their areas equals the ratio of
the lengths of their altitude
53
In an iscosceles right triangle, the hypotenuse is ________ times as long as each of the legs.
√2
54
Which of the following is not a secondary part of a triangle?
Sides
55
Which of the following is not a property of a triangle?
The sum of two sides is less than the third side
56
Given the sides of a triangle as 3m and 5m. The third side is
from 3m to 7m
57
A straight from the vertex of a triangle to the midpoint of the opposite side is known as
median
58
Indicate the false statement:
Three or more lines which have one point in common are said to be coplanar.
59
The case of the solution of the triangle in the plane where the given data lead to two solutions.
Ambiguous case
60
The most proved theorem in Mathematics
Pythagorean theorem
61
The least proved theorem in Mathematics.
Fermat's last theorem
62
Equations used for checking the solution to a plane triangle using law of sine's are as follows: (a+b)/c=cos(1/2)(A-B)/sin(1/2)C and (a-b)/c=sin(1/2)(A-B)/cos(1/2)C. These equations are called
Mollweide's equations
63
Napier's rule states that the sine of any middle part is equal to the product of the ____ of the adjacent parts.
cosine
64
Napier's rule states that the sine of any middle part is equal to the product of the __________ of the adjacent parts.
tangent
65
How many formulas may be derived from using Napier's Rules?
10
66
The sum of all interior angles in a spherical triangle is always
greater than 180° but less than 540°
67
The maximum value for the longitude is
180°
68
If R is the radius of a sphere and E is an spherical excess (in radians), then the area of a spherical triangle is
R^2E
69
One minute of the great circle arc on the surface of the earth is equivalent to
1 nautical mile
70
A spherical triangle with at least one side is a quarter of a great circle is called ______ spherical triangle.
trirectangular
71
One of the two great circles intersecting at right angle at the piles and dividing equinoctial points and ecliptic into 4 parts.
Colure
72
The radius of the earth used in spherical trigonometry is
3959 statute miles
73
The difference between a nautical mile and a statute mile.
800 ft
74
Manila has a longitude of 121°°05'E. What is the time difference between Manila and Greenwich l, England which is at prime meridian?
8 hrs and 4 mins
75
The earth is divided into how many time zone?
24
76
In a spherical triangle, two angles (or side) are on the same species if they are both.
between 0° and 90° or both between 90° and 180°
77
Spherical degree is a unit of a spherical area taken as 1/720 of the surface of the sphere. Howany spherical degrees a hemisphere have?
360°
78
Which of the following statements is false about spherical trigonometry?
The sum of all interior angles of a spherical triangles is 360°
79
The sum of the sides of a spherical triangles is always less than
360°
80
The sum of any two angles of a spherical triangle is
less than 180° + the third angle
81
Refers to the angular distance from the equator measured along meridian.
Latitude
82
Refers to the angle at either pole between the meridian passing through a point and some fixed meridian known as the prime meridian.
Longitude
83
Is half if a great circle terminated by the North Pole and South Pole.
Meridian
84
When the hypotenuse of a right spherical triangle is less than 90°.
the two legs are on the same quadrant
85
When the hypotenuse of a right spherical triangle is greater than 90°>
one leg is one the first quadrant and the other on the second quadrant
86
The point where a ray from the center of the earth through an observer's position on it intersects the celestial sphere is call the observer's
zenith
87
The point that is diametrically opposite the zenith is called
nadir
88
The great circles through the north and south celestial poles are called
hour circles and celestial meridian
89
An oblique equilateral parallelogram:
rhombus
90
Mil is a unit of
angle and length
91
The maximum value of a latitude is
90°
92
A spherical triangle with all angles equals to a right triangle is called _____ spherical triangle?
birectangular