Trigonometry

The earliest recorded use of statistics was in the 5th century BCE. The ancient Greeks were attempting to scale a wall, and determined the necessary height for their ladders by counting the bricks in the wall. Since that time, the science of statistics has expanded to include both the collection of the data and the mathematical analysis thereof.

The slope of the line y = -2 is zero.

No one in particular because trigonometry has evolved over thousands of years with many ancient and modern mathematicians making their own discoveries and contributions to the subject.

We live on a sphere. Calculating 'shortest' distance on the sphere is not a simple trig problem, you may need spherical trig.

In the 1st column make a list of numbers, and in the 2nd column calculate the tangent of each value in the 1st column. Try entering 0.01 in A1 and =A1+0.01 in A2, then select A2:A942 and fill down. In B1 enter =tan(A1), then select B1:B942 and fill down. Next, select A1:B942, then insert a line graph. Adjust the Y axis range until it looks good.

Because he was credited with working out the mathematics behind it.

the only soluton is regular practice.Pravtice makaes a man perfect.First be thorough with the book uypu have been prescribed with then try out with references.

After 12 hours, the first boat is at a distance 14*12 = 168 miles east of the port.

The second boat is at a distance

28*12*cos(30) = 291.0 miles north

and

28*12*sin(30) = 168.0 miles east

of the port.

Since their Eastward displacement is the same, the distance between the two is the Northwards displacement of the second boat = 291.0 miles.

that cannot be proved because it is not necessarily true.

A sine wave has no harmonics. It only has a fundamental, so the value of the 2nd, 3rd, and 12th harmonics of a sine wave is zero.

The tangent function, perhaps. Tan is an Ant that is messed up.

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

they can be, depending on the information that you are given. If you know lengths of sides, then YES.

There are many ways of finding angles in triangles...one of which is to get a protractor, of course...

Also, if you know two angles, you can find the third by just subtracting the sum of the two angles from 180, which is the total number of degrees in any triangle.

same as a rectangle, i.e. 2(l+b)

The cosine function has an absolute value that cannot exceed 1. Therefore the is no angle x such that cos(x) = 3.

That is, there is no angle x such that x = cos^-1(3).

density x volume

math proffessers, mathematicians, archetecs, engineers, surveers, sructual design, deolition supervisors, rocket scientists

* * * * *

or try spelling them as professors, archiitects, surveyors, structural design, demolition supervisors.

There are also actuarists, statisticians, econometricians, physicists, meteorologists and many other careers.

How to move a specific distance along a line determined by 2 points in 3d space!

Specific distance = m

Distance between the 2 points = D

Distance to move along line from Point #2 toward Point #1 = Displacement = m

Determine the coordinates of the point M (c, d, e), which is m units closer to Point#2

Given 2 points

Point #1 (a, b, c)

Point #2 (g. h, i)

1. Find the distance between the 2 points using Pythagorean Theorem

Think of moving from Point #1 to Point #2 by moving along the x-axis, then the y-axis, then the z-axis.

(g-a) = distance moved along the x-axis

(h-b) = distance moved along the y-axis

(i-c) = distance moved along the x-axisS

D = [(g-a)^2 + (h-e)^2 + (i-c)^2]^0.5

2. Determine the coordinates of the unit vector by dividing the distance moved along each axis by D.

Coordinates of unit vector = [(g-a) ÷ D], [(h-b) ÷ D], [(i-c) ÷ D]

x coordinate of unit vector = (g-a) ÷ D

y coordinate of unit vector = (h-b) ÷ D

z coordinate of unit vector = (i-c) ÷ D

Unit vector = [((g-a) ÷ D)^2 + ((h-e) ÷ D) ^2) + ((i-c) ÷ D) ^2]^0.5) = 1

If the value of the unit vector does not =1, go back and check your work.

3. Multiply each coordinate of the unit vector by m to determine the coordinates of the vector m. These coordinates will be added to coordinates of Point #1 to determine the coordinates of Point #3.

x coordinate of m vector = m * (g-a) ÷ D

y coordinate of m vector = m * (h-b) ÷ D

z coordinate of m vector = m * (i-c) ÷ D

4. To determine the coordinates of Point #3(d, e, f) that is m cm from Point #1 toward Point #2, add the coordinates of the m vector to the coordinates of Point #1.

d = x coordinate of Point #3 = a + (m * (g-a) ÷ D)

e = y coordinate of Point #3 = b + (m * (h-b) ÷ D)

f = z coordinate of Point #3 = c + (m * (i-c) ÷ D)

5. To determine the distance from Point #1 (a, b, c) to Point #3 (d, e, f), use Pythagorean Theorem

D = [(d-a)^2 + (e-b)^2 + (f-c)^2]^0.5

The answer should be m.

I wanted to move 2 cm from Point #1 toward Point #2, and I did.

Now let's see if this method works!! Point #1 = (2,3,1), Point #2 = (6,9,3)

I want to move 2 cm from Point #1 toward Point #2, that means m = 2 cm.

1. Find the distance between the 2 points using Pythagorean Theorem

D = [(g-a)^2 + (h-e)^2 + (i-c)^2]^0.5

D = [(6-2)^2 + (9-3)^2 + (3-1)^2]^0.5

D = [(4)^2 + (6)^2 + (2)^2]^0.5

D = [16 + 36 + (4)]^0.5

D = 56^0.5

D = 7.4833

So the line between these Point #1 and Point #2 is 7.483 units long

2. Determine the coordinates of the unit vector by dividing the distance moved along each axis by D.

Distance moved along x-axis = 4

Distance moved along y-axis = 6

Distance moved along z-axis = 2

x-coordinate of unit vector = 4 ÷ 7.4833 = 0.5345

y-coordinate of unit vector = 6 ÷ 7.483 = 0.8018

z-coordinate of unit vector = 2 ÷ 7.483 = 0.2673

Length of unit vector = [(0.5345)^2 + (0.8018)^2+ (0.2673)^2]^0.5 = 1

The length of the unit vector should = 1

3. Multiply each coordinate of the unit vector by m to determine the coordinates of the vector m.

x coordinate of m vector = m * (g-a) ÷ D = 2 * 0.5345 = 1.069

y coordinate of m vector = m * (h-b) ÷ D = 2 * 0.8018 = 1.6036

z coordinate of m vector = m * (i-c) ÷ D = 2 * 0.2673 = 0.5346

m vector = [1.069^2 + (1.6036)^2 + (1.5346)^2]^0.5 = 2

4. To determine the coordinates of the Point #3 (d, e, f) that is m cm from Point #1 toward Point #2, add the coordinates of the m vector to the coordinates of Point #1 (a, b, c).

Point #1 = (2, 3, 1)

x coordinate of Point #3 = 2 + 1.069 = 3.069

y coordinate of Point #3 = 3 +1.6036 = 4.6036

z coordinate of Point #3 = 1+ 0.5346 = 1.5346

Point #3 = (3.069, 4.6036, 1.5346)

5. To determine the distance from Point#1 to Point #3, use Pythagorean Theorem

D = [(d-a)^2 + (e-b)^2 + (f-c)^2]^0.5

D = [(3.069-2)^2 + (4.6036-3)^2 + (1.5346-1)^2]^0.5

D = [(1.069)^2 + (1.6036)^2 + (0.5346)^2]^0.5 = 2

D = 2 cm

I wanted to move 2 cm from Point #1 toward Point #2, and I did.

tan(141 deg) = -0.8098 approx.

a2 - b2 = (a - b)(a + b)

Study hard, check your work.

There are four kinds of relations in ordered pairs:

one to one (each x value is unique and has a unique y value associated with it)

one to many (each x value has multiple possible y values)

many to one (each y value has multiple possible x values)

many to many (x and y values can be repeated and are not unique)

See the related link for more helpful information.

cos2x + 2sinx - 2 = 0

(1-2sin2x)+2sinx-2=0

-(2sin2x-2sinx+1)=0

-2sinx(sinx+1)=0

-2sinx=0 , sinx+1=0

sinx=0 , sinx=1

x= 0(pi) , pi/2 , pi