Trigonometry

sin A cos B – cos A sin B is equivalent to:

Sin ( A – B )

The angular distance of a point on the terrestrial sphere from the north pole is called

Coaltitude

Csc 520° is equal to

Csc 20°

What is the sine of 820°?

0.984

The logarithm of the negative number is

Imaginary

The sum of the squares of the sine and cosine of an angle.

1

The logarithm of a number to the base ( 2.7182.... ) is called

Napierian logarithm

The characteristic is equal to the exponent of

10, when the number is written in

Logarithmic form

Napierian logarithms have a base

closest to which number?

2.72

A logarithm of 1 to any base is

Zero

Sin ( 270 + β ) is equal to

- Cos β

The sum of the angles in an octant

spheric triangle is

270°

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 midpoint which is called the

Centroid

The altitudes of the sides of the triangle

intersects at the point known as

Orthocenter

The angle which the line of sight to the object makes

with the horizontal which is above the eye of the

observer is called

Angle of elevation

Log M – Log N is equal to

Log M/N

The other form of log⌄a N = b is

N = a^b

The point of concurrency of the

altitude of the triangle.

Orthocenter

The point of concurrency of the perpendicular

bisector of the sides of the triangle.

Circumcenter

The point of concurrency of the angle

bisector of the triangle is called

Incenter

The logarithm of the reciprocal of N is

called ______ of N

Cologarithm

The inverse function of a logarithm is

known as

Antilogarithm

The cologarithm of a number is the

_______ of the logarithm of a number.

Negative

The first table logarithm with 10 as

base was developed in 1615 by

Henry Briggs

Who invented logarithms in 1614?

John Napier

The number loga b is called the ____ of the system

of a base a with respect to the system of base b.

Modulus

Napierian logarithm has a base of

e

Log x = _____ ln x.

0.434

ln x = _____ log x.

2.303

Which of the following cannot be a

base of a logarithm?

1

The integral part of a common

logarithm is

Characteristic

The mantissa of a logarithm is a

Positive value or zero

For 0 < x < 1, ln x is

Negative

If 1 < N < 10, then

1 < log N < 2

To change log⌄a to log⌄b N, multiply log⌄a N by

log⌄b a

The numbers log⌄a b to log⌄b a are

Reciprocal of each other

Logarithm using 10 as base.

Common logarithm

The logarithm of a product is the __________ of the

logarithms, and the logarithm of a quotient is the

__________ of the logarithms.

Sum, difference

When a logarithm is expressed as an integer plus

a decimal (between 0 and 1), the integer is called

Characteristics

The characteristics of a logarithm is 3.

the number between

1000 and 10000

The characteristics of the common

logarithm of a number greater than 1 is

Zero or positive

The characteristics is __________ the exponent of 10,

when the number is written scientific notation.

Equal to

If the logarithm to base 10 (denoted as log10) is called

common logarothm is called natural logarithm, what do

you call the logarithm of base 2 (denotes as lb)?

Binary logarithm

If the unknown is a conditional equatio occur as an

exponent, the best way to solve the unknown is by

Taking the logarithm of both sides

Angles of rotation with the same

initial side and terminal side.

Co-terminal angles

An angle equal to one revolution of

360°

Perigon

The angle which the line of sight to the object makes

with the horizotal is above the eye of an observer.

Angle of elevation

A triangle inscribed in a given triangle whose vertices

are the feet of the three perpendiculars to the sides of

the same point inside, the given triangle.

Pedal triangle

The triangle with minimum perimeter but maximum

area inscribed in another triangle is known as

Pedal triangle

A right triangle whose length of sides may

be expressed as the ratio of integral units.

Primitive triangle

A triangle with no side equal is known

as

Scalene triangle

If two triangles have congruent bases, then

the ratio of their areas equals the ratio of

The lengths of their altitudes

In an isosceles right triangle, the hypotenuse is

__________ times as long as each of the legs.

√ 2

Which of the following is not a

secondary part of a triangle?

Sides

Which of the following is not a

property of a triangle?

The sum of two sides is less than the third side.

Given the sides of a triangle as 3m

and 5m. The third side is

From 3m to 7m

A straight from the vertex of a triangle to the

midpoint of the opposite side is known as

Median

Indicate the false statement:

Three or more lines which have one point in

common are said to be coplanar.

The case of the solution of the triangle in the

plane where the given data leads to two solutions.

Ambigous case

The most proved theorem in

mathematics.

Pythagorean theorem

The least proved theorem in

mathematics.

Fermat’s last theorem

Equations used for checking the solution to a plane triangle using law of

sine’s as follows:

(a+b)/c = (cos1/2 (A + B)) / (sin1/2 C) and

(a-b)/c = (sin1/2 (A - B)) / (cos1/2 C). These equations are called

Mollweide’s equations

Napier’s rule states that the sine of any middle part is

equal to the product of the __________ of the

opposite parts.

Cosine

Napier’s rule states that the sine of any middle part is

equal to the product of the __________ of the adjacent

parts.

Tangent

How many formulas may be derived

from using the Napier’s rules?

10

The sum of all interior angles in a

spherical triangle is always

Greater than 180° but less than 540°

The maximum value for the longitude

is

180°

The maximum value for the latitude is

90°

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

One minute of the great circle arc on the

surface of the earth is equivalent to

1 nautical mile

A spherical triangle with all angles equal to a right

triangle is called __________ spherical triangle.

Birectangular

A spherical triangle with at least one side is a quarter of

a great circle is called __________ spherical triangle.

Trirectangular

One of the two great circles intersecting at right angle

at the piles and dividing equinoctial points and ecliptic

into 4 parts.

Colure

The radius of the earth used in

spherical trigonometry is

3959 statute miles

The difference between a nautical

mile and a statute mile.

800 feet

Manila has a longitude of 121°05’E. What is the time

difference between Manila and Greenwich, England

which is at prime meridian?

8 hours 4 minutes

The earth is divided into how many

time zone?

24

In a spherical triangle, two angles (or sides)

are on the same species if they are both

Between 0° and 90°

or both Between 90°

and 180°

Spherical degree is a unit of a spherical area taken as

1/720 of the surface of the sphere. How many spherical

degrees a hemisphere have?

360°

Which of the following statements is

false about spherical trigonometry?

The sum of all interior angles of a spherical triangles

is 360°

The sum of the sides of a spherical

triangles is always less than

360°

The sum of any two angles of a

spherical triangle is

Less than 180° + the third angle

Refers to the angular distance from the

equator measured along a meridian.

Latitude

Refers to the angle at either pole between the meridian

passing through a point and some fixed meridian

known as the prime meridian.

Longitude

Is half of a great circle terminated by

the north pole and south pole.

Meridian

When the hypotenuse of a right

spherical triangle is less than 90°

The two legs are on the same quadrant

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

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

The point that is diametrically

opposite the zenith is called

Nadir

The great circles through the north

and south celestial poles are called

Hour circle and Celestial meridians

An oblique equilateral parallelogram:

Rhombus

Mil is a unit of

Angle and length