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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 is the contribution of Georg Von Purbach in trigonometry?
In Epytoma…in Almagestum Ptolomei, the abridgment of Ptolemy's Almagest which was completed by his student, Regiomontanus, he replaced chords by sines, and calculated tables of sines for every minute of arc for a radius of 600,000 units. He made his observations with very simple instruments, using an ordinary plumb-line to measure the angles of elevation of the stars. He also introduced a mathematical innovation by using Hindu-Arabic numerals in his sine tables, the first transition from the duodecimal to the decimal system. Peuerbach noted several errors in Ptolemy's calculations, but remained a devotee of the ancient Greek mathematician.
(the side opposite the angle) divided by (the side adjacent to the angle) = tangent of the angle
(the side opposite the angle) divided by (the hypotenuse of the triangle) = sine of the angle
(the side adjacent to the angle) divided by (the hypotenuse of the triangle) = cosine of the angle
Once you have the sine OR the cosine OR the tangent of the angle, you can get the measurement of the angle on a scientific calculator, or look it up in a table of trig functions in a book.
Check out these articles for a simple free tool and tutorial that will make trig simple enough for ANYBODY to understand!
http://www.ehow.com/how_5520340_memorize-trig-functions-losing-mind.html
http://www.ehow.com/how_5227490_pass-mind-part-unknown-sides.html
http://www.ehow.com/how_5428511_pass-part-ii-unknown-angles.html
Write z equals 8 in trigonometric form?
When z = 8, z lies straight along the real axis, so r = 8 and theta = 0°
9,3,6 The dimensions given above would not be suitable for a right angled triangle which presumably the question is asking about. The dimensions suitable for a right angled triangle in the question are: 9, 12, 15.
Slope is rise divided by run and percent is rise divided by run then multiply by 100 to change to % slope. As a check to your data, (3.2/40)*100 does equal 8%, so it is confirmed correct. You simply have a right triangle with height of 3.2, length of 40, and the length of the hypotenuse needs to be found to answer the question. The solution is sqrt(3.22+402) which is 40.1278 ft.
What is the definition of bearing trigonometry?
The bearing of a point B, from a point A, is based on the angle that the straight line AB makes with the line AN which goes due North from A. The angle is measured in the clockwise direction and is normally expressed as a 3 digit number (including leading zeros).
HOW TO find the area of right angle triangle?
Simple. Just multiply the base by the height of the triangle, and divide it into two. This works for all types of triangles.
There are a lot of videos and applets out there that explain how to construct an angle bisector.
3 mathematicians who contributed the development of Trig?
The branch of mathematics called trigonometry studies the relationships of lengths and angles of triangles. Three mathematicians who contributed to the development of trigonometry are: Pythagoras, Joseph Fourier, Norman J. Wildberger.
What are facts about The alps?
The Swiss Alps (located on the border between France, Switzerland, and Italy) are Europe's highest mountain range, and have Europe's highest peak, Mont Blanc.
Who are the fathers of trigonometry?
There is no one or two or a few 'fathers of trigonometry.' Ancient Sumarians, Babalonians started using ratios of sides of triangles. The Greeks continued the study, but emphasized geometric methods instead of algebraic methods that used in trig. Egyptians, Persians, Arabic, and Indians all contributed to the development of trig. This whole process took about 2000 years, maybe more.
What is the world's longest math lesson?
I would imagine that learning the numbers of Pi up to a certain point, like maybe 1000 numbers, would be the longest math lesson, in a sense.
If you go through the basics of math may be you can't feel that any math lesson as longest math lesson in world.
What is the horizontal acceleration of a projectile?
The horizontal acceleration i.e. Vx throughout the trajectory remains constant only of the air resistance is neglected. The gravity can affect the y-component of velocity but is unable to affect its x-component. Acceleration (delta V) does not occur unless a change comes into play per Newton. Gravity does not effect x but air resistance would. Likewise, projectiles launched from e.g. an explosion experience a reducing delta V in that acceleration from an explosion is subject to the inverse square rule.
What is the number of units needed to cover a surface enclosed by a geometric figure?
The answer is Area. The answer is Area.
Why do acoustics need trigonometry?
When people are taught trigenometry in school it is usually just for finding the angles of a triangle. But the sine and cosine functions are actually waves if you were to draw them on a graph. Acoustics is sound waves, and by mapping sound waves into trigonometric waves we can do calculations on them like addition.
What is the function of a ligament in relation to movement?
Ligaments provide stability to a joint during both rest and movement. Excessive movements such as hyper-extension or hyper-flexion can be restricted by ligaments. Also, ligaments prevent movements in some directions.
Enumerate the applications of trigonometry of different fields?
Trigonometry is used in many jobs! Trigonometry is used in forestry(to calculate height of trees), A variety of Engineering jobs, Coast Guards and Flight Coordinators use Trigonometry with vector math to deal with movement through water/air currents. Carpenters need to know basic trigonometry. Any job dealing with any type of waves(sound waves, the pattern that the tide follows) has to know about Trigonometric Functions. I could keep listing jobs but the basics are:
1) any job that involves practical design(meaning not fashion design)
2) any job that requires basic physics or calculus
3) any job that requires basic high school math
Trigonometry shows up everywhere, in order to be good with numbers, you have to be good with trigonometry
geometry in real life as the statement seems is just simply geometry in real life if we observe carefully in our everyday surrondings such as the shape of trees ,cars ,houses and even our own human body we can observe geometry for eg. most houses are rectangular in shape etc.
Generally pre-calculus is taken after trigonometry, unless the trigonometry course was supplemented by a pre-calculus course, in which case the next course would be calculus.
Where can you source the tools to hold the camshaft and crankshaft on a 94 Mark VIII?
Autozone has a loan a tool program, did you check there yet? You leave a deposit, use their tool and return it to get your deposit back. They don't lend out brand named tools like Mac and Snap-on and their tools are not th ebest but I have used them to get by on projects when funds run short and I am unable to buy the tool I need.
When do you actually use geometry in life outside of school?
It is very important that we as a human race do not become too dependant upon computers to do everything for us to the point of that, if they quit working for us, we would be lost. Thus the reason for the seemingly mundane. Furthermore, geometry is more of a building block (no pun intended) in preperation for the higher mathematics such as algebra, trig, calc and differiential equations. All of these maths are used frequently by engineers in conjunction with the computer programs they use. Whether it be designing a road (civil), designing a drill chuck (mechanical) or creating a 3D structure of an atom (chemical) . . . when using computers, it always pays to put the same mathematical ideas upon paper in order to broaden the perspectives and understandings of what and how the engineer is trying to accomplish their goals.
How do you calculate radius vectors?
According to http://mathworld.wolfram.com/RadiusVector.html the radius vector (often written as r hat, or the letter r with a carrot ^ over it) is just the distance from the origin to the point of interest.
So the magnitude is the distance between the point and the origin, and the direction is the direction from the origin to the point.
This is a ballistic motion problem. A 30-kg ball -- man, that's one heavy damn ball -- is kicked at an angle of 45 degrees to the horizontal and travels a distance of 20 meters. Well, aside from a broken toe, what can we determine? If I recall from trajectory/ballistics problems, the range of a projectile is given by the following formula: R = 2VxVy/g, where Vx and Vy are the horizontal and vertical components of the velocity, respectively. Vx = VcosA and Vy = VsinA, where A is the take-off angle, 45 degrees in this case. That is very convenient, because both components are, therefore, equal in magnitude: Vx = Vy = V/SQRT(2). So, making the substitutions into the equation above, we get R = V2/g. Solving for V, we get V = SQRT(Rg). Substituting, we get V = SQRT(196) = 14 (m/s). Note how the mass of the ball had no bearing on the answer. I decided to fiddle a bit more with the problem and use only the basic formulas used in high-school physics that deal with displacement (distance), velocity, and acceleration. The main formula for calculating displacement, d, is: d(t) = do + Vot + (1/2)at2, where do is the initial displacement, Vo is the initial velocity, and a is acceleration. And there is one other basic formula that will come in handy later: V(t) = Vo + at. In English, that means the velocity at any time, t, can be found by multiplying the acceleration by t and adding it to the initial velocity. For this problem, there are two main equations, one for displacement in the horizontal direction, dx, and one for displacement in the vertical direction, dy. For both we assume that the initial displacement, do, is zero, since the initial point of flight -- the kick-off point -- is the origin and represents zero displacement in either direction (x or y). So, dox = doy = 0. We also know there is no acceleration in the xdirection, and the acceleration in the y direction is the acceleration due to gravity, g, which is negative, that is, directed downward. So, dx(t) = dox + Voxt + (1/2)at2 = 0 + Voxt + 0 = Voxt
and
dy(t) = doy + Voyt + (1/2)at2 = 0 + Voyt - (1/2)gt2 = Voyt - (1/2)gt2
So, we have the following: (Equ. 1) dx(t) = Voxt
and (Equ. 2) dy(t) = Voyt - (1/2)gt2
But we must now get our brains around a few observations and facts of the problem. Since the take-off angle is 45 degrees to the horizontal, we know that the horizontal and vertical components of the initial velocity are equal in magnitude. (Their directions, of course, are perpendicular to each other.) So, we can write Vox = Voy. This fact will come in handy later. We also know that at some later time, T, the ball will strike the ground 20 meters away. So, substituting for d and t in Equ. 1 above, we have 20 = VoxT. Solving for T, we write: (Equ. 3) T = 20/Vox Further, we also know that the ball reaches the highest point in its trajectory half way through its trip, at t = T/2. And we also know that at its highest point, the vertical velocity is zero. Recall the earlier formula: V(t) = Vo + at. That will be useful now. Using that formula, we can write the equation for the velocity in the vertical direction like this: Vy(t) = Voy - gt And since we already established that the vertical velocity is zero at t = T/2, the equation becomes: Vy(T/2) = Voy - g * (T/2) = 0 Solving for T, we get: (Equ. 4) T = 2Voy/g But now we have two independent equations (Equ. 3 and Equ. 4) for T, which is very cool. We can now write: 20/Vox = 2Voy/g Rearranging the terms, we can write: VoxVoy = 10g But since Vox = Voy, we can write V2 ox = 10g, or Vox = SQRT(10g) = SQRT(98) = 9.9. Uh-oh, that's not 14, like we calculated earlier. Nope, it isn't. That's because we calculated only the x component of the velocity. The magnitude of the velocity of the ball is the vector sum of the x and ycomponents. Since they are equal and at right angles to each other, we can easily use the Pythagorean theorem to calculate it: V2 = V2ox + V2oy V = SQRT(V2ox + V2oy) V = SQRT(10g + 10g) = SQRT(196) = 14 m/s. Bingo!
Divide metres by seconds. In this case, 110m/72s= 1.53 m/s.
