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Worksheets

Trigonometry

Total questions: 92

Worksheet time: 47mins

Name
Class
Date
1.

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

a)

cos (A - B)

b)

sin (A - B)

c)

tan (A - B)

d)

cos 2 (A - B)

2.

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

a)

Coaltitude

b)

Latitude

c)

Altitude

d)

Codeclination

3.

Csc 520° is equal to

a)

cos 20°

b)

csc 20°

c)

tan 45°

d)

sin 20°

4.

What is the sine of 820°?

a)

0.984

b)

0.866

c)

-0.866

d)

-0.5

5.

The logarithm of the negative number is

a)

Imaginary

b)

Irrational

c)

Real

d)

Rational

6.

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

a)

0

b)

1

c)

2

d)

3

7.

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

a)

Napierian logarithm

b)

Characteristic

c)

Mantissa

d)

Briggsian logarithm

8.

The characteristic is equal to the exponent of 10, when the number is written in

a)

Exponential form

b)

Scientific notation

c)

Logarithmic form

d)

Irrational number

9.

Naperian logarithms have a base closest to which number?

a)

2.72

b)

2.82

c)

2.92

d)

10

10.

The logarithm of 1 to any base is

a)

Indeterminate

b)

Zero

c)

Infinity

d)

One

11.

Sin (270° + ß) is equal to

a)

-cos ß

b)

sin ß

c)

-sin ß

d)

cos ß

12.

The sum of the angles in an octant spheric triangle

a)

180°

b)

270°

c)

360°

d)

540°

13.

The median of a triangle is the line connecting the vertex and the midpoint of the opposite side. For given triangle, these medians intersects at a point which is called the

a)

Orthocenter

b)

Circumcenter

c)

Centroid

d)

Incenter

14.

The altitudes of the sides of the triangle intersects at the point known as

a)

Orthocenter

b)

Incenter

c)

Centroid

d)

Circumcenter

15.

The angle which the line of sight to the object makes with the horizontal which is above the eye of the observer is called

a)

Angle of depression

b)

Angle of elevation

c)

Acute angle

d)

Bearing

16.

Log M - log N is equal to

a)

Log MN

b)

Log (m-N)

c)

Log (M/N)

d)

Log (N - M)

17.

The other form of loga N = b is

a)

N = ba

b)

N = ab

c)

N = ab

d)

N = a/b

18.

The point of concurrency of the altitude of the triangle

a)

Orthocenter

b)

Centroid

c)

Metacenter

d)

Incenter

19.

The point of concurrency of the perpendicular bisector of the sides of the triangle

a)

Orthocenter

b)

Circumcenter

c)

Centroid

d)

Incenter

20.

The point of concurrency of the angle bisector of the triangle is called

a)

Orthocenter

b)

Circumcenter

c)

Centroid

d)

Incenter

21.

The logarithm of the reciprocal of N is called the ______ of N

a)

Antilogarithm

b)

Cologarithm

c)

Natural logarithm

d)

Briggsian logarithm

22.

The inverse function of a logarithm is known as

a)

Antilogarithm

b)

Cologarithm

c)

Antiderivative

d)

Antecedent

23.

The cologarithm of a number is the ______ of the logarithm of a number

a)

Positive

b)

Absolute value

c)

Negative

d)

Reciprocal

24.

The first table logarithms with 10 as base was developed in 1615 by

a)

James Naismith

b)

Henry Briggs

c)

John Napier

d)

John Wallis

25.

Who invented logarithms in 1614?

a)

John Wallis

b)

Henry Briggs

c)

John Napier

d)

L'Hospital

26.

The number logab is called the _______ of the system of a base a with respect to the system of base b

a)

Coefficient

b)

Logarithm

c)

Modulus

d)

Exponent

27.

Napierian logarithm has a base of

a)

π

b)

10

c)

1

d)

e

28.

Log x = ____ ln x

a)

0.434

b)

10

c)

2.303

d)

e

29.

ln x = ____ log x

a)

0.434

b)

10

c)

2.303

d)

e

30.

Which of the following cannot be a base for a logarithm

a)

10

b)

π

c)

1

d)

e

31.

The integral part of a common logarithm

a)

10

b)

e

c)

Mantissa

d)

Characteristic

32.

The mantissa of a logarithm is a

a)

Positive value only

b)

Negative value only

c)

Positive value, negative value or zero

d)

Positive value or zero

33.

For 0 < 0 < 1, ln x is

a)

Positive

b)

Zero

c)

Negative

d)

Between 0 and 1

34.

If 1 < N < 10, then

a)

1 < log N < 2

b)

0 < log N < 1

c)

2 < log N < 3

d)

-1 < log N < 0

35.

To change loga to logb N, multiply loga N by

a)

Loga b

b)

Logb a

c)

LogN a

d)

Logn b

36.

The numbers loga b and logb a are

a)

Equal

b)

Equal but different in signs

c)

Reciprocal to each other

d)

Negative reciprocal to each other

37.

Logarithm using 10 as base

a)

Decimal logarithm

b)

Scientific logarithm

c)

Common logarithm

d)

Natural logarithm

38.

The logarithm of a product is the _____ of the logarithms and the logarithm of the quotient is the ____ of the logarithms

a)

Sum, difference

b)

Difference, sum

c)

Quotient, product

d)

Product , quotient

39.

When the logarithm is expressed as a integer plus a decimal (between 0 and 1), the integer is called

a)

Briggsian logarithm

b)

Napierian logarithm

c)

Mantissa

d)

Characteristic

40.

The characteristic of a logarithm is 3. The number between

a)

1 and 10

b)

10 and 100

c)

100 and 1000

d)

1000 and 10000

41.

The characteristics of the common logarithm of a number greater than 1 is

a)

Zero

b)

Positive

c)

Negative

d)

Zero or positive

42.

The characteristic is _____ the exponent of 10, when the number is written in scientific notation

a)

Equal to

b)

Greater than

c)

Less than

d)

None of the above

43.

If logarithm to base 10 (denoted as log10) is called common logarithm, what do you call the logarithm of base 2 (denotes as lb)?

a)

Binary logarithm

b)

Bit logarithm

c)

Bilogarithm

d)

All of the above

44.

If the unknown is a conditional equation occurs as an exponent, the best way to solve the unknown is by

a)

Raising the power of both sides

b)

Taking the logarithm of both sides

c)

Extracting the root of both sides

d)

Applying the Newton's method

45.

Angles of rotation with the same initial side and terminal side

a)

Terminal angles

b)

Conjugate angles

c)

Coterminal angle

d)

Supplementary angles

46.

An angle equal to one revolution of 360°

a)

Perigon

b)

Explement angle

c)

Reflex angle

d)

Supplement angle

47.

The angle which the line of sight of the object makes with the horizontal is below the eye of an observer

a)

Angle of depression

b)

Angle of elevation

c)

Acute angle

d)

Bearing

48.

A triangle inscribed in a given triangle whose vertices are the feet of the three perpendiculars to the sides from same point inside the given triangle

a)

Inscribed triangle

b)

Primitive triangle

c)

Pedal triangle

d)

Obtuse triangle

49.

The triangle with minimum perimeter but maximum area inscribed in another triangle is known as

a)

Pedal triangle

b)

Euclid's triangle

c)

Primitive triangle

d)

None of the above

50.

A right triangle whose length of sides may be expressed as a ratio of integral units

a)

Pedal triangle

b)

Isosceles triangle

c)

Scalene triangle

d)

Primitive triangle

51.

A triangle with no side equal is known as

a)

Acute triangle

b)

Oblique triangle

c)

Equilateral triangle

d)

Scalene triangle

52.

If two triangles have congruent bases, then the ratio of their areas equals the ratio of

a)

Their perimeter s

b)

The lengths of their altitudes

c)

Their sides

d)

None of the above

53.

In an isosceles right triangle, the hypotenuse is ____ times as long as each of the legs

a)

√2

b)

√3

c)

2

d)

3

54.

Which of the following is not a secondary part of a triangle?

a)

Attitudes

b)

Medians

c)

Exterior angles

d)

Sides

55.

Which if the following is not a property of a triangle?

a)

The sum of the three angles is always equal to two right angles

b)

The sum of two sides is less than the third side

c)

If the two sides are equal, the angles opposite are unequal

d)

The altitudes of the triangle meet in a point

56.

Given the sides of a triangle as 3m and 5m. The third side is

a)

Between 3m and 8m

b)

Greater than 8m

c)

From 3m to 7m

d)

From 2m to 8m

57.

A straight from the vertex of a triangle to the midpoint of the opposite side is known as

a)

Altitude

b)

Median

c)

Height

d)

A or B

58.

Indicate the false statement:

a)

An altitude of a triangle is a perpendicular drop from any vertex to the opposite side

b)

Three or more lines whuch have one point in common are said to be coplanar

c)

The altitudes of a triangle meet in a point

d)

A locus is a figure containing all the points and only those which fulfill a given requirement

59.

The case of the solution of the triangle in the plane where the given data lead to two solutions

a)

Axioms of Euclid

b)

Absurb case

c)

Ambigous case

d)

All of the above

60.

The most proved theorem in mathematics.

a)

Gauss lemma

b)

Fermat's theorem

c)

Ptolony's theorem

d)

Pythagorean theorem

61.

The least proved theorem in mathematics

a)

Goldbach conjecture

b)

Fermat's last theorem

c)

Mersenne's proportion

d)

Pappus proportions

62.

Equations used for checking the solution to a plane triangle using law of sine's are as follows. These equations are called

a)

Diophantine equations

b)

Mollweide's equations

c)

Mohr equations

d)

Gauss equations

63.

Napier's rule states that the sine of any middle part is equal to the product of the _____ of the opposite parts

a)

Sine

b)

Cosine

c)

Tangent

d)

Secant

64.

Napier's rule states that the sine of any middle part is equal to the product of the _____ of the adjacent parts

a)

Sine

b)

Cosine

c)

Tangent

d)

Cotangent

65.

How many formulas may be derived from using the Napier's rules?

a)

5

b)

6

c)

8

d)

10

66.

The sum of all interior angles in a spherical triangle is always

a)

Greater than 180° but less than 270°

b)

Greater than 180° but less than 360°

c)

Greater than 180° but less than 540°

d)

Greater than 270° but less than 540°

67.

The maximum value for the longitude is

a)

90°

b)

180°

c)

45°

d)

360°

68.

The maximum value for a latitude is

a)

90°

b)

45°

c)

180°

d)

360°

69.

If R is the radius of a sphere and E is the spherical excess (in radians), then the area of a spherical triangle is

a)

πR2E

b)

R2E

c)

½R2E

d)

R²/E

70.

One minute of the great circle arc on the surface of the earth is equivalent to

a)

1 statue mile

b)

1 nautical mile

c)

60 statue mile

d)

60 nautical mile

71.

A spherical triangle with all angles equals to a right triangle is called ____ spherical triangle

a)

Birectangular

b)

Quandrantal

c)

Trirectangular

d)

Right

72.

A spherical triangle with at least one side is a quarter of a great circle is called ____ spherical triangle

a)

Octant

b)

Quadrantal

c)

Trirectangular

d)

Birectangular

73.

One of the two great circles intersecting at right angle at the poles and dividing equinoctial points and ecliptic into 4 parts

a)

Nadir

b)

Zenith

c)

Declination

d)

Colure

74.

The radius of the earth used in spherical trigonometry is

a)

3989 statue miles

b)

3979 statue miles

c)

3969 statue miles

d)

3959 statue miles

75.

The difference between a nautical mile and a statue mile

a)

800 feet

b)

900 feet

c)

1000 feet

d)

500 feet

76.

Manila has a longitude of 121°05'E. What us the time difference between Manila and Greenwich, England which is at the prime meridian

a)

8 hours and 40 minutes

b)

8 hours and 34 minutes

c)

8 hours and 14 minutes

d)

8 hours and 4 minutes

77.

The earth is divided into how many time zone?

a)

24

b)

18

c)

16

d)

12

78.

In a spherical triangle, two angles (or sides) are on the same species if they are both

a)

Between 0° and 180°

b)

Between 0° and 90°

c)

Between 90° and 180°

d)

Between 0° and 90° or both between 90° and 180°

79.

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?

a)

360°

b)

720°

c)

180°

d)

270°

80.

Which if the following statements is false about spherical trigonometry?

a)

If two angles of a spherical triangle are equal, the sides opposite are equal and conversely

b)

If two angles of a spherical triangle are unequal, and the greater side lies opposite the greater angle, and conversely

c)

The sum of two sides of a spherical triangle is greater than the third sides

d)

The sum of all interior angles of a spherical triangles is 360°

81.

The sum of the sides of a spherical triangles is always less than

a)

270°

b)

360°

c)

540°

d)

180°

82.

The sum of any two angles of a spherical triangle is

a)

Greater than 180°

b)

Less than 180°

c)

Less than 180° + the third angle

d)

Greater than 180° + the third angle

83.

Refers to the angular distance from the equator measured along a meridian

a)

Longitude

b)

Latitude

c)

Meridian

d)

Declination

84.

Refers to the angle at either pole between the meridian passing through a point and some fixed meridian known as the prime meridian

a)

Longitude

b)

Latitude

c)

Declination

d)

Meridian

85.

Is half of a great circle terminated by the North Pole and South Pole

a)

Longitude

b)

Latitude

c)

Declination

d)

Meridian

86.

When the hypotenuse of a right spherical triangle is less than 90°

a)

The two legs are on the same quadrant

b)

The two legs are on the different quadrant

c)

One leg is on the first quadrant and the other on the second quadrant

d)

None of the above

87.

When the hypotenuse of a right spherical triangle is greater than 90°

a)

The two legs are on the same quadrant

b)

The two legs are on the different quadrant

c)

One leg is one the first quadrant and the other on the second quadrant

d)

None of the above

88.

The point where a ray from the center of the earth through an observer's position on it intersects the celestial sphere is called the observer's

a)

Zenith

b)

Nadir

c)

Pole

d)

Equinox

89.

The point that is diametrically opposite the zenith is called

a)

Pole

b)

Equinox

c)

Nadir

d)

Celestial meridian

90.

The great circles through the north and south celestial poles are called

a)

Hour circles

b)

Celestial meridians

c)

Elevated poles

d)

A and B

91.

An oblique equilateral parallelogram

a)

Square

b)

Rectangle

c)

Rhombus

d)

Trapezoid

92.

Mil is a unit of

a)

Angle

b)

Length

c)

Angle and length

d)

Weight