Font size
WorksheetsTrigonometry
Total questions: 92
Worksheet time: 47mins
Sin A cos B – cos A sin B is equivalent to:
cos (A - B)
sin (A - B)
tan (A - B)
cos 2 (A - B)
The angular distance of a point on the terrestrial sphere from the north pole is called
Coaltitude
Latitude
Altitude
Codeclination
Csc 520° is equal to
cos 20°
csc 20°
tan 45°
sin 20°
What is the sine of 820°?
0.984
0.866
-0.866
-0.5
The logarithm of the negative number is
Imaginary
Irrational
Real
Rational
The sum of the squares of the sine and cosine of an angle
0
1
2
3
The logarithm of a number to the base e (2.7182...) is called
Napierian logarithm
Characteristic
Mantissa
Briggsian logarithm
The characteristic is equal to the exponent of 10, when the number is written in
Exponential form
Scientific notation
Logarithmic form
Irrational number
Naperian logarithms have a base closest to which number?
2.72
2.82
2.92
10
The logarithm of 1 to any base is
Indeterminate
Zero
Infinity
One
Sin (270° + ß) is equal to
-cos ß
sin ß
-sin ß
cos ß
The sum of the angles in an octant spheric triangle
180°
270°
360°
540°
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
Orthocenter
Circumcenter
Centroid
Incenter
The altitudes of the sides of the triangle intersects at the point known as
Orthocenter
Incenter
Centroid
Circumcenter
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 depression
Angle of elevation
Acute angle
Bearing
Log M - log N is equal to
Log MN
Log (m-N)
Log (M/N)
Log (N - M)
The other form of loga N = b is
N = ba
N = ab
N = ab
N = a/b
The point of concurrency of the altitude of the triangle
Orthocenter
Centroid
Metacenter
Incenter
The point of concurrency of the perpendicular bisector of the sides of the triangle
Orthocenter
Circumcenter
Centroid
Incenter
The point of concurrency of the angle bisector of the triangle is called
Orthocenter
Circumcenter
Centroid
Incenter
The logarithm of the reciprocal of N is called the ______ of N
Antilogarithm
Cologarithm
Natural logarithm
Briggsian logarithm
The inverse function of a logarithm is known as
Antilogarithm
Cologarithm
Antiderivative
Antecedent
The cologarithm of a number is the ______ of the logarithm of a number
Positive
Absolute value
Negative
Reciprocal
The first table logarithms with 10 as base was developed in 1615 by
James Naismith
Henry Briggs
John Napier
John Wallis
Who invented logarithms in 1614?
John Wallis
Henry Briggs
John Napier
L'Hospital
The number logab is called the _______ of the system of a base a with respect to the system of base b
Coefficient
Logarithm
Modulus
Exponent
Napierian logarithm has a base of
π
10
1
e
Log x = ____ ln x
0.434
10
2.303
e
ln x = ____ log x
0.434
10
2.303
e
Which of the following cannot be a base for a logarithm
10
π
1
e
The integral part of a common logarithm
10
e
Mantissa
Characteristic
The mantissa of a logarithm is a
Positive value only
Negative value only
Positive value, negative value or zero
Positive value or zero
For 0 < 0 < 1, ln x is
Positive
Zero
Negative
Between 0 and 1
If 1 < N < 10, then
1 < log N < 2
0 < log N < 1
2 < log N < 3
-1 < log N < 0
To change loga to logb N, multiply loga N by
Loga b
Logb a
LogN a
Logn b
The numbers loga b and logb a are
Equal
Equal but different in signs
Reciprocal to each other
Negative reciprocal to each other
Logarithm using 10 as base
Decimal logarithm
Scientific logarithm
Common logarithm
Natural logarithm
The logarithm of a product is the _____ of the logarithms and the logarithm of the quotient is the ____ of the logarithms
Sum, difference
Difference, sum
Quotient, product
Product , quotient
When the logarithm is expressed as a integer plus a decimal (between 0 and 1), the integer is called
Briggsian logarithm
Napierian logarithm
Mantissa
Characteristic
The characteristic of a logarithm is 3. The number between
1 and 10
10 and 100
100 and 1000
1000 and 10000
The characteristics of the common logarithm of a number greater than 1 is
Zero
Positive
Negative
Zero or positive
The characteristic is _____ the exponent of 10, when the number is written in scientific notation
Equal to
Greater than
Less than
None of the above
If logarithm to base 10 (denoted as log10) is called common logarithm, what do you call the logarithm of base 2 (denotes as lb)?
Binary logarithm
Bit logarithm
Bilogarithm
All of the above
If the unknown is a conditional equation occurs as an exponent, the best way to solve the unknown is by
Raising the power of both sides
Taking the logarithm of both sides
Extracting the root of both sides
Applying the Newton's method
Angles of rotation with the same initial side and terminal side
Terminal angles
Conjugate angles
Coterminal angle
Supplementary angles
An angle equal to one revolution of 360°
Perigon
Explement angle
Reflex angle
Supplement angle
The angle which the line of sight of the object makes with the horizontal is below the eye of an observer
Angle of depression
Angle of elevation
Acute angle
Bearing
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
Inscribed triangle
Primitive triangle
Pedal triangle
Obtuse triangle
The triangle with minimum perimeter but maximum area inscribed in another triangle is known as
Pedal triangle
Euclid's triangle
Primitive triangle
None of the above
A right triangle whose length of sides may be expressed as a ratio of integral units
Pedal triangle
Isosceles triangle
Scalene triangle
Primitive triangle
A triangle with no side equal is known as
Acute triangle
Oblique triangle
Equilateral triangle
Scalene triangle
If two triangles have congruent bases, then the ratio of their areas equals the ratio of
Their perimeter s
The lengths of their altitudes
Their sides
None of the above
In an isosceles right triangle, the hypotenuse is ____ times as long as each of the legs
√2
√3
2
3
Which of the following is not a secondary part of a triangle?
Attitudes
Medians
Exterior angles
Sides
Which if the following is not a property of a triangle?
The sum of the three angles is always equal to two right angles
The sum of two sides is less than the third side
If the two sides are equal, the angles opposite are unequal
The altitudes of the triangle meet in a point
Given the sides of a triangle as 3m and 5m. The third side is
Between 3m and 8m
Greater than 8m
From 3m to 7m
From 2m to 8m
A straight from the vertex of a triangle to the midpoint of the opposite side is known as
Altitude
Median
Height
A or B
Indicate the false statement:
An altitude of a triangle is a perpendicular drop from any vertex to the opposite side
Three or more lines whuch have one point in common are said to be coplanar
The altitudes of a triangle meet in a point
A locus is a figure containing all the points and only those which fulfill a given requirement
The case of the solution of the triangle in the plane where the given data lead to two solutions
Axioms of Euclid
Absurb case
Ambigous case
All of the above
The most proved theorem in mathematics.
Gauss lemma
Fermat's theorem
Ptolony's theorem
Pythagorean theorem
The least proved theorem in mathematics
Goldbach conjecture
Fermat's last theorem
Mersenne's proportion
Pappus proportions
Equations used for checking the solution to a plane triangle using law of sine's are as follows. These equations are called
Diophantine equations
Mollweide's equations
Mohr equations
Gauss equations
Napier's rule states that the sine of any middle part is equal to the product of the _____ of the opposite parts
Sine
Cosine
Tangent
Secant
Napier's rule states that the sine of any middle part is equal to the product of the _____ of the adjacent parts
Sine
Cosine
Tangent
Cotangent
How many formulas may be derived from using the Napier's rules?
5
6
8
10
The sum of all interior angles in a spherical triangle is always
Greater than 180° but less than 270°
Greater than 180° but less than 360°
Greater than 180° but less than 540°
Greater than 270° but less than 540°
The maximum value for the longitude is
90°
180°
45°
360°
The maximum value for a latitude is
90°
45°
180°
360°
If R is the radius of a sphere and E is the spherical excess (in radians), then the area of a spherical triangle is
πR2E
R2E
½R2E
R²/E
One minute of the great circle arc on the surface of the earth is equivalent to
1 statue mile
1 nautical mile
60 statue mile
60 nautical mile
A spherical triangle with all angles equals to a right triangle is called ____ spherical triangle
Birectangular
Quandrantal
Trirectangular
Right
A spherical triangle with at least one side is a quarter of a great circle is called ____ spherical triangle
Octant
Quadrantal
Trirectangular
Birectangular
One of the two great circles intersecting at right angle at the poles and dividing equinoctial points and ecliptic into 4 parts
Nadir
Zenith
Declination
Colure
The radius of the earth used in spherical trigonometry is
3989 statue miles
3979 statue miles
3969 statue miles
3959 statue miles
The difference between a nautical mile and a statue mile
800 feet
900 feet
1000 feet
500 feet
Manila has a longitude of 121°05'E. What us the time difference between Manila and Greenwich, England which is at the prime meridian
8 hours and 40 minutes
8 hours and 34 minutes
8 hours and 14 minutes
8 hours and 4 minutes
The earth is divided into how many time zone?
24
18
16
12
In a spherical triangle, two angles (or sides) are on the same species if they are both
Between 0° and 180°
Between 0° and 90°
Between 90° and 180°
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°
720°
180°
270°
Which if the following statements is false about spherical trigonometry?
If two angles of a spherical triangle are equal, the sides opposite are equal and conversely
If two angles of a spherical triangle are unequal, and the greater side lies opposite the greater angle, and conversely
The sum of two sides of a spherical triangle is greater than the third sides
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
270°
360°
540°
180°
The sum of any two angles of a spherical triangle is
Greater than 180°
Less than 180°
Less than 180° + the third angle
Greater than 180° + the third angle
Refers to the angular distance from the equator measured along a meridian
Longitude
Latitude
Meridian
Declination
Refers to the angle at either pole between the meridian passing through a point and some fixed meridian known as the prime meridian
Longitude
Latitude
Declination
Meridian
Is half of a great circle terminated by the North Pole and South Pole
Longitude
Latitude
Declination
Meridian
When the hypotenuse of a right spherical triangle is less than 90°
The two legs are on the same quadrant
The two legs are on the different quadrant
One leg is on the first quadrant and the other on the second quadrant
None of the above
When the hypotenuse of a right spherical triangle is greater than 90°
The two legs are on the same quadrant
The two legs are on the different quadrant
One leg is one the first quadrant and the other on the second quadrant
None of the above
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
Zenith
Nadir
Pole
Equinox
The point that is diametrically opposite the zenith is called
Pole
Equinox
Nadir
Celestial meridian
The great circles through the north and south celestial poles are called
Hour circles
Celestial meridians
Elevated poles
A and B
An oblique equilateral parallelogram
Square
Rectangle
Rhombus
Trapezoid
Mil is a unit of
Angle
Length
Angle and length
Weight
