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Trigonometry
Trigonometry is a field of mathematics. It is the study of triangles. Trigonometry includes planar trigonometry, spherical trigonometry, finding unknown values in triangles, trigonometric functions, and trigonometric function graphs.
3,810 Questions
What are the 2 ways of measuring angles?
you can use a protractor or the paper test to see if the angle is a right angle
Degrees and radians.
the founder thinks that how to relate the perpendicular triangle's sides.so that in that way he found the trigonometry.
What's the square root of 3 times the square root of 15?
3.4086580994024981055126631335409
sqrt(3)= 1.7320508075688772935274463415059
sqrt(15) = 3.8729833462074168851792653997824
sqrt(3) x sqrt(15) = 6.7082039324993690892275210061938 = sqrt(45) = 3 x sqrt(5)
AnswerThis is an example of a question that's ambiguous because it hasn't been written mathematically. The above answer is for sqrt(3) x sqrt(15). Another interpretation of the question would be sqrt(3 x sqrt(15)), which has a different answer.What are the six functions of a dollar?
1. What will the value of a dollar grow to in n periods at i interest?
(Table #1 = Future value of a dollar)
2. What will a dollar set aside at the beginning of each year accumulate to after n periods at i interest?
(Table #2 = Accumulation of a dollar per period)
3. How much must be set aside in each of n periods at i interest in order to reach a specific sum in the future?
(Table #3 = Sinking fund factor)
4. What is the value today of a dollar received n periods in the future if one's opportunity cost is i?
(Table #4 = Present value of a dollar)
5. What is the value of the right to receive a dollar each of the next n periods if opportunity cost is i?
(Table #5 = Present value of an ordinary annuity)
6. What instalment payment is required to amortize a debt of one dollar over n periods at i interest?
(Table #6 = Installment to amortize a dollar)
- Trigonometry is the study of triangles.
- The name comes from Greek trigonon "triangle" + metron "measure".
- The field emerged during the 3rd century BC from applications of geometry to astronomical studies.
Trigonometry is a branch of mathematics that solves problems relating to plane and spherical triangles. Its principles are based on the fixed proportions of sides for a particular angle in a right-angled triangle, the simplest of which are known as the sine, cosine, and tangent (so-called trigonometric ratios). Trigonometry is of practical importance in navigation, surveying, and simple harmonic motion in physics. The sine and cosine functions are the co-ordinates of a point on the unit circle as a function of the angle made by a ray from the center to the point and turn out to be of fundamental importance in complex analysis.
Law of sines and cosines in mathematics?
Consider a triangle with vertices A, B and C. Call the edge opposite a given vertex by the same letter, but lower case. So side a is opposite vertex A etc.
Law of Sines says:
SinA/a= SinB/b=SinC/c
If you prefer, you can split the equation into multiple separate ones:
SinA/a=SinB/b
Sin A/a=SinC/c etc.
(there is one more part of the law of Sines which most books leave out. If R is the radius of a circumcircle around triangle ABC, then SinA/a= SinB/b=SinC/c =2R and in case you forgot a circumcirlce of a triangle is a unique circle that passes through each of the triangle 3 vertices.)
The law of Cosines says:
a2 +b2 -2abCosC=c2
or a2 +b2 -2abCosB=b2
or a2 +b2 -2abCosA=a2
How do you solve for side b in a right triangle when angle a is 40 degrees and the hypotenuse is 15?
I'll take a shot at this, but it's all assumptions and guesswork, since the question is so ambiguous:
-- The question doesn't state how many sides the figure has, or whether the 'b' is an angle or a side.
-- Assume that we're working with a right triangle, because the question uses the word "hypotenuse".
-- Assume that the 'b' it's asking for is another angle, besides the 40-degree angle given.
-- If it's a triangle, then the sum of the 3 interior angles is 180 degrees.
-- If it's a right triangle, then one of the interior angles is 90 degrees.
-- The missing angle is [ 180 - 90 - 40 ] = 50 degrees.
The length of the hypotenuse makes no difference, but we're very happy that
you said the magic word "hypotenuse".
What is the area of right angled triangle at the right?
There is no right triangle on the right! (Ignore the length of the hypotenuse of a right triangle.) if you have the length of the two legs (base and the upright side): (base x upright) ÷ 2 = area of the right angle triangle.
How do you find the circumference of the earth using the arc length formula?
Just did this in my trig class yesterday.
Arc length = radius * theta(radians)
Circumference of Earth = radius of earth * 2pi
Note: The arc length is the circumference of the Earth only in this case because theta is equal to 2pi.
Where does the word costamonger come from?
The spelling should be costermonger, and it refers to a street seller of fruit and veg. It's thought to derive from the name of a type of apple, costard, and monger (vendor). It's particularly associated with the east-end of London.
Who are the mathematicians that developed trigonometry?
The first recorded use of trigonometry came from the Hellenistic mathematician Hipparchus circa 150 BC, who compiled a trigonometric table using the sine for solving triangles. Ptolemy further developed trigonometric calculations circa 100 AD
Development of trigonometry is not the work of any one man or nation. It first originated in India and the basic concepts of angle and measurements was noted in Vedic texts such as Srimad Bhagavatam. However, trigonometry in its present form was established in Surya Siddhanta and later by Aryabhata [5th century CE]. It should be noted that from the time of Hipparchus until modern times there was no such thing as a trigonometric ratio. Instead, the Indian civilization and after them the Greeks and the Muslims used trigonometric lines.
Pythagoras of Samos (580? BC- 500? BC) was an Ionian Greek mathematician and also founder of the religious movement called Pythagoreanism.
Nasir al-Din al-Tusi (1135-1213) (aka Sharafeddin Tusi) widely promulgated studies in trigonometry, which was compiled by him as a new subject in its own right for the first time. He also developed the subject of spherical trigonometry.
How do you make a homemade clinometer?
Way One - Buy a plastic protractor or make one from cardboard. Tape a standard drinking straw to the straight edge of the protractor. This will be your scope. Attach string to the straw at the 0 degree mark. Tie a light weight to the string. You can use a washer or a screw or anything else that can balance the clinometer and be unobtrusive. Sight a tall object to make sure the clinometer was constructed correctly
Way Two - Fold a "square" piece of paper in half from corner to corner and crease, it to form two triangles with one 90 degree angle and two 45 degree angles, and leave it folded together so that it appears to be one triangle. Tape or glue the triangles together so that they will not open back up to make it stronger. Note: Thicker paper, such as construction paper or poster board will make your clinometer more durable. The paper that you use must be square so that both sides (called legs) of the triangle are equal length.
Tape a straight drinking straw to the triangle's hypotenuse. Position a drinking straw along the hypotenuse (the longest edge of the triangle) so that one end extends slightly out from the paper, and use tape or glue to secure it to the paper. The straw will be the sight that you look through. Make sure you don't deform the straw, and make sure that it is aligned perfectly on top (along the edge) of the hypotenuse.
Punch a small hole close to the corner where the hypotenuse meets either side. The hypotenuse, of course, meets both of the other sides. You should put the hole near the corner where the straw does not extend beyond the paper (this will be the top of the clinometer).
Insert a string through the hole and tie a knot or tape it to keep it from slipping out of the hole. Use enough string so that you have at least a few inches dangling at the bottom of the clinometer.
Tie a washer or fishing weight to the bottom end of the string. The weight should dangle a few inches below the corner of the clinometer so that the string will swing freely. Use one eye to look at the top of some tall object, such as a tree or pole, through the straw.
For such an object, you can back up or move forward while the weight always points straight downward and when the string lines up with the leg
of the triangle and it will be 45 degrees, reading on the clinometer. When this happens, it means the angle of elevation between your eye and the top of the object is 45 degrees.
The obvious answer is the relationships between the sides and angles of triangles. Waves in the sea are an example of a sine wave. Tidal Experts and Meterologists alike use sine waves to help predict tides. Music will also emit waves that may often look like a sine wave and pure notes will look like sine or cosine waves. The speed of a swinging pendulum can be plotted as a sine wave as well as the sound of a tuning fork.
What is the rules of subtracting integers?
if substracting by two negatives your going to add ex: -2-(-5) it would be positive 7.
if your substracting with two differ numbers it you would substract and take the sign the sign of the biggest number.ex: 2+(-3) it would be-1 sice 3 is bigger than2 you take the sign of 3
What is the most common way trig is used in everyday life?
Global Positioning Systems (GPS) use trigonometry. There are a number of satellites orbiting the earth. The GPS uses the time signals sent by these satellites to establish the distance to the satellites. Trigonometry is then used to find the location of the GPS unit.
What is cosine's law how can solve this type of question?
In a triangle with vertices A, B and C and sides a, b and c where a lower case side is opposite the upper case vertex,
a^2 = b^2 + c^2 - 2*b*c*Cos(A).
The second part of the question cannot be answered since "this type of question" is not described!
Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "times", "equals", "squared", "cubed" etc.
Having said that, the equation in the question cannot represent a solid since it has only two variables: a solid needs three.
How can you say that the relation is a function?
A relation is a function if every value in the domain is mapped to only one value in the range.
A non-mathematical example is mothers. Leaving aside surrogacy, every person has only one mother. Therefore the relation
f(x) = x's mother is a function.
But f(x) = x's ancestor is not a function because everyone has loads of ancestors. They may not all be known but that is not relevant.
If a boat is 50 meters away from a lighthouse what is the height?
Not enough information has been given to answer this question such as what is the angle of elevation?
What are the contributions of Johann muller in trigonometry?
REGIOMONTANUS (1436-1476), German astronomer, was born at Konigsberg in Franconia on the 6th of June 1436. The son of a miller, his name originally was Johann Muller, but he called himself, from his birthplace, Joh. de Monteregio, an appellation which became gradually modified into Regiomontanus. At Vienna, from 1452, he was the pupil and associate of George Purbach (1423-1461), and they jointly undertook a reform of astronomy rendered necessary by the errors they detected in the Alphonsine Tables. In this they were much hindered by the lack of correct translations of Ptolemy's works; and in 1462 Regiomontanus accompanied Cardinal Bessarion to Italy in search of authentic manuscripts. He rapidly mastered Greek at Rome and Ferrara, lectured on Alfraganus at Padua, and completed at Venice in 1463 Purbach's Epitome in Cl. Ptolemaei magnam compositionem (printed at Venice in 1496), and his own De Triangulis (Nuremberg, 1533), the earliest work treating of trigonometry as a substantive science. A quarrel with George of Trebizond, the blunders in whose translation of the Almagesthe had pointed out, obliged him to quit Rome precipitately in 1468. He repaired to Vienna, and was thence summoned to Buda by Matthias Corvinus, king of Hungary, for the purpose of collating Greek manuscripts at a handsome salary. He also finished his Tabulae Directionum(Nuremberg, '475), essentially an astrological work, but containing a valuable table of tangents. An outbreak of war, meanwhile, diverted the king's attention from learning, and in 1471 Regiomontanus settled at Nuremberg. Bernhard Walther, a rich patrician, became his pupil and patron; and they together equipped the first European observatory, for which Regiomontanus himself constructed instruments of an improved type (described in his posthumous Scripta, Nuremberg, 1544). His observations of the great comet of January 1472 supplied the basis of modern cometary astronomy. At a printing-press established in Walther's house by Regiomontanus, Purbach's Theoricae planetarum novaewas published in 1472 or 1473; a series of popular calendars issued from it, and in 1474 a volume ofEphemerides calculated by Regiomontanus for thirty-two years (1474-1506), in which the method of "lunar distances," for determining the longitude at sea, was recommended and explained. In 1472 Regiomontanus was summoned to Rome by Pope Sixtus IV. to aid in the reform of the calendar; and there he died, most likely of the plague, on the 6th of July 1476.
How do you convert radians per second to meters per second?
the tangential velocity is equal to the angular velocity multiplied by the radius the tangential velocity is equal to the angular velocity multiplied by the radius
