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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
How do you find the angle of trajectory to hit a point at a different height with a set velocity?
How do you find the angle of trajectory to hit a point at a different height with a set velocity? You will need to know the horizontal distance to the point!! Think about it. The farther it is to the point, the greater the velocity has to be. The maximum distance for any set velocity is at an angle of 45º. If the velocity is too small, the object will not reach the point no matter even at 45º. So I will use Dh to be the horizontal distance to the point.
I will send you this tonight, but tomorrow I will input values for the velocity, the different height, and the distance horizontal. I will send it again if I find any mistakes.
V = set velocity
Different height =Distance vertical =Dv
Eq. #1 Total distance moved = Vi* t + ½ * at^2
When an object is thrown up into the air, a = acceleration due to gravity =g = -9.8m/s^2
Eq. #2 Distance vertical = V * sin θ* time - (½ * 9.8 * t^2)
½ * 9.8 = 4.9
You can substitute the values of Dv into Eq. #3, to reduce the number of variables. However, I will continue to derive the total equation for the angle.
Eq. #3 Dv = (V * sin θ* t) - (4.9 * t^2)
Range = Distance horizontal = Dh
Eq. #4 Distance horizontal = V * cos θ * time
You can substitute the values of Dh into Eq. #5, to reduce the number of variables. However, I will continue to derive the total equation for the angle.
Eq. #5 Dh = V * cos θ * t
If we solve both equations for V and set them equal to each other, we can solve for t. The time is the same for the Dh and Dv, because these distances are the same for the same one and only object.
From Eq. #3, Dv = (V * sin θ* t) - (4.9 * t^2)
Eq. #6 Dv + (4.9 * t^2) = V * sin θ* t
Eq. #7 V = [ Dv + (4.9 * t^2) ] ÷ (sin θ* t )
From Eq. #5 Dh= V * cos θ * t
Eq. #8 V = Dh ÷ (cos θ * t)
We have 2 equations equal to V. set them equal to each other.
Eq. #9 [ Dv + (4.9 * t^2) ] ÷ (sin θ* t ) = Dh ÷ (cos θ * t)
You may not believe this, but the equation above is a proportion!!
Cross multiply
[ Dv + (4.9 * t^2) ] * (cos θ * t) =Dh * (sin θ * t)
I see factor of t on both sides. Cancel it out.
Eq. #10 [ Dv + (4.9 * t^2) ] * (cos θ) =Dh * (sin θ)
I can multiply (cos θ) * Dv + (4.9 * t^2) ] =
Eq. #11 (Dv * (cos θ) + (cos θ) * 4.9 * t^2) = Dh * (sin θ)
I need t on the left side
Eq. #12 (cos θ) * 4.9 * t^2) = Dh * (sin θ) - (Dv * (cos θ)
Now we will divide both sides by (cos θ * 4.9)
Eq. #13 t^2 = (Dh *sin θ - Dv * cos θ) ÷ (cos θ * 4.9)
You know the value Dh and Dv in Eq. #13.
Solve for t = [(Dh *sin θ - Dv * cos θ) ÷ (cos θ * 4.9)]^0.5
(Square root of t^2)
Eq. #14 t = [(Dh *sin θ - Dv * cos θ) ÷ (cos θ * 4.9)]^0.5
Now substitute the value of Dh, V, and t into the Eq. #5 and find cosθ.
Eq. #5 Dh = V * cos θ * t
Eq. #15 cos θ = Dh ÷ (V * t)
cos θ = Dh ÷ (V * t)
Eq. #16 cos θ = Dh ÷ [ V * [(Dh * sin θ - Dv * cos θ) ÷ (cos θ * 4.9)]^0.5]
Eq. #17 θ = cos^-1 [Dh ÷ [ V * [(Dh * sin θ - Dv * cos θ) ÷ (cos θ * 4.9)]^0.5] ]
The motion of the baseball is parabolic. So, the ball was at the different height twice as it moved along the parabola. The different height would be occurs at 2 places as the baseball follows the parabolic path, once on the way up and once on the way down. The value of the distance horizontal determines the answer; up or down A short Dh would produce a small value of t and a large value of Dh would produce a large value of t.
From Eq. #9 [ Dv + (4.9 * t^2) ] ÷ (sin θ * t ) = Dh ÷ (cos θ * t), we can see that Dh only affects time.
That is why Dh is so critical to the answer for θ.
How many edges are in a octohedron?
An octahedron (not octohedron) is a polyhedron with 8 faces. There are 257 distinct topological octahedrons and the number of vertices and edges varies.
For example, an octahedron in the form of a quadrilateral based bipyramid has only 12 edges whereas a hexagonal prism has 18.
How are geometry and trigonometry different?
Geometry is the study of spatial properties (shapes, sizes, etc.), while trigonometry is the study of triangles and the relationships between angles and lengths.
How do you learn cos sin and tan formulas?
I guess you are meaning the standard trigonometric ratios regarding the cos/sin/tan of angles in a right angled triangle.
I was taught this little rhyme:
Two Old Arabs
Soft Of Heart
Coshed Andy Hatchett
Using the initial letters of each of the words:
T O A
S O H
C A H
Gives:
Tan = Opposite / Adjacent
Sin = Opposite / Hypotenuse
Cos = Adjacent / Hypotenuse
Later I met the nonsense word SOHCAHTOA (pronounced So-ka-toe-ah or Sock-a-toe-ah) in which the letters are the ratios as before and which is slightly more useful in that in that order it gives a reminder that Sin/Cos = Tan. However, it does require being able to spell the unusual "word".
it is a shape with 4 parellel lines and it slanted on one side
How is finding the area of a rhombus similar to finding the area of a kite?
Because in both cases their diagonals cross at right angles
So their areas are: 0.5*product of diagonals
Change is usually the value of an expression before some operation subtracted from the value after the operation. Occasionally, subtraction may be replaced by division.
How do you put in sine on a calculator?
Most scientific calculators come with a button that says SIN, or they have it under a secondary option usually accessed by pressing the SHIFT or 2ND first then the key sub labeled SIN.
What are extra dimensional beings?
They are living "things" from a space of more dimensions than the 3 dimensions of space and 1 of time that we live in and are aware of.
What are the effects of changing the values of a b and c in the equation y equals af x b c?
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".
What number must you add to complete the square x2 4x 7?
Put in the - or + values for 4x and 7 is the first step in finding the number needed
How do you calculate arc sine?
arc sine is the inverse function of the sine function so if y = sin(x) then x = arcsin(y) where y belongs to [-pi/2, pi/2].
It can be calculated using the Taylor series given in the link below.
The answer depends on the shape whose surface area for which a formula is required.
What are the formulas that include the changes of degree to radian?
To convert from degrees to radians, multiply the number of degrees by (pi / 180). Pi is approximately 3.1416.
sin(3x) = -sqrt(3)/2
so 3x = 240 + k*360 degrees or 300 + k*360 degrees where k is any integer
so that x is 80+120k or 100+120k degrees.
Where does the word railroad come from?
Railroad and railway are both words referring to 'tracked' roads, where a guides (rails) keep the wheeled vehicle on a specific route. The earliest known reference to the word "railroad" is in 1757 and referred to a mine tram on wooden rails and moved either by animals or men. Tracked tramways have been around since antiquity.
The usage for modern railroads hauling freight and people is from the 1820's.
Railroad is a typical American English usage. Railway is more typical British American usage. However there is considerable crossover is usage. For example the "South Pacific Railway Company" (1887) was originally incorporated as the "South Pacific Railroad Company" (1876).
The
How are cranes removed from the roof of tall buildings?
From what I have read: The crane "grows" using a jib, hydraulics, and sections. When the building is completed, the arms are dissassembled on the roof (they may be removed by another crane attached to a truck, or by other equipment on the roof?), and the process is then reversed (each section removed floor by floor by equipment inside the building). The jib is lowered as each section is removed, until there is nothing left, and the jib assembly is removed at ground level. I may need correction on this one though
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Is a sine function a periodic function?
Yes, the sine function is a periodic function. It has a period of 2 pi radians or 360 degrees.
"Sonya Kovalevsky (1850-1891) was a Russian mathematician. She received her Ph.D from the University of Gottingen for her thesis on partial differential equations. In 1888 she won the Bodin Prize for her memoir on the rotation of a solid body about a fixed point." Excerpted from the Columbia Encyclopedia, 6th. Edition 2007
What is the origin of the word is?
Check any good dictionary (not a small paperback). The word has roots that include Old High German "ist", Old Norse "es", Gothic "ist", Latin "est, and the infinitive esse", Greek "esti", Sanskrit "asti", and Hittite "aszi". A wonderful lineage for such an unassuming [and powerful] word.
