Math and Arithmetic

The square root of a right angle is 45º. Take, for example the √i=a+bi. Squaring both sides gives i=a²+2abi+b²i². Then, a²-b²+(2ab-1)i=0. Resolving for a²-b²=0 and 2ab-1=0, results in √i=(1+i)/√2. This is a 45º vector of magnitude 1/√2.

The relationship is:

1 degree (°) = 60 minutes (60′)

1 minute (1′) = 60 seconds (60″)

So:

1° = 60′ = 3,600″

1′ = 1/60 of a degree

1″ = 1/3,600 of a degree

For example:

2° 30′ means 2.5 degrees.

15′ means 0.25 degrees.

This unit is commonly used in geography (latitude and longitude), astronomy, and surveying to measure angles precisely.

Since '141' is an odd number it will NOt divide by the first prime number' '2'.

So try the next prime number, which is '3'.

Hence

3)141 =47

Since '47' is a prime number, there are no other factors of '141'

Sso the factor tree is 1,3,47,141.

1.5 x 10^(2)

If 9 batteries cost 27 dollars, then the cost of each battery can be calculated by dividing the total cost by the number of batteries. Therefore, each battery costs 27 dollars ÷ 9 batteries = 3 dollars per battery.

500000000000000⁰0000000000000

100 cm^(3) / 1000000 cm^(3) = 1/10000 m^(3) = 0.0001 m^(3) or 1.0 x 10^(-4) m^(3)

Remember there are 1,000,000 cm^(3) = 1 m^(3)

In words ' 'one million cm^(3) = one cubic metre'.

So to convert cubic metres to cm^(3) , multiply by 1,000,000 ( one million).

NB To convert cm^(3) to cubic metres (m^(3)) , divide by 1,000,000 ( one million0.

Remember

Linear ; 100 cm = 1 m

Area ; 100 cm x 100 cm = 10,000 cm^2 = 1 m^(2)

Volume ; 100 cm x 100 cm x 100 cm = 1000000 cm^(3) = 1 m^(3)

That is 'one million cm^(2) makes one cubic metre.

Since there 100,000 cm^(3)

Then

100000/1000000 = 1/10 = 0.1 m^(3)

Hence one hundred thousand cm^(3) makes for 'one tenth' of a cubic metre.

Is this a serious question?If you can't figure out that the answer is 48 then you're really,really dumb.

I mean, anyone old enough to type is old enough to figure that out...

It is: 3994+10 = 4004

A twenty-sided shape in 2D is called a icosagon. It is a polygon with twenty edges and twenty vertices. The term comes from the Greek words "icosa," meaning twenty, and "gon," meaning angle.

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First of all it is spelled as 'Cosine' , and shortened to 'Cos'.

pi and has the approximate value . 3.141592.....

Hence

Cos(pi) = Cos( 3.141592.... ) = 1.0 ( On calculators it may shown 0.998.... , this is because the value of 'pi' is only approximate.

As a decimal: 0.866

As a fraction: √(3)/2

Although you learn the trig. functions between 0 - 90 , they are a continuous 'wave'; from negative infinity to positive infinity.

So you can put in any degrees value into a Sin/Cos function, and the answer will always be between '-1 & 1'.

e/.g/ Sin ( 1080 ) = 0

Cosine ( 1080 ) = 1.

So for 180 degrees. the sine function rises from 0 to 90 and then fall back from 90 - 180

Sine(180) = 0 .

Cos (180) = -1

Tan(180) = 0

Csc180) = 1/ Sin = 1/0 ( undefined)

Sec( 180) = 1/Cos = 1/-1 = -1

Cot( 180) = Cos/Sin = 1/0 ( undefined(.

Sin(45 ) = 1/Sqrt(2) = 0.7071....

Cos(45) = 1/Sqrt(2) = 0.7071...

Tan(45) = 0.7071.../0.7071... Cancel down = '1'

Cosecant(45) = 1/Sin(45) = 1/ [1/sqrt(2) = sqrt(2) = 1.4142....

Secant (45) = 1/Cos(45) = 1/ [1/sqrt(2) = sqrt(2) = 1.4142....

Cotangent = Cos/Sin = 0.7071... / 0.7071... = 1.

The principal Trigonometric function is Sine(Sin).

It has a complementary function Cosine (Cos).

Bases on these two functions, are further trig. functions. they are.

Tangent(Tan) = Sin /Cos

Cosecant(CSC) = 1/Sin

Secant (SEC) = 1/Cos

Cotangent(COT) = Cos/Sin

The word 'Sine' comes from Latin , and means 'curve'. Initially you learn it between 0 - 90 degrees. It is a continuous 'wave', from infinity to infinity. .

The Sin/Cos functions only range from -1 to 1 through '0'.

The Tan function ranges from negative infinity to positive infinity, through '0'.

For a triangle inscribed in a circle.

At the circles centre, the radius may be '1' unit. If the radius is angles at 30 degrees from the horizontal(x) axis, then the vertical (opposite) lines perpendicular height of the triangle is exactly '1/2' ( 0.5), compared to the radius.

Hence the Sin( 30 degrees) is opposite / radius(hypotenuse) = (1/2)/1 = 1/2

All the othesr trig. functional answer are based on moving the radius from horizontal to vertical. with in the described circle. This is why it produces , such 'horrible' decimal figures.

Have a look in Castle's Four Figures Tables, rather than using a pocket calculator, and also graphs of the Sine/Cosine and Tangent curves.

12

Just divide by 2

Well, isn't that a happy little math problem! When you multiply 15 by 3, you get 45. Just imagine those numbers dancing together on the canvas of your mind, creating a beautiful equation that brings a smile to your face. Let's paint some happy little numbers today!

Negative four thirds multiplied by nine sevenths equals negative twelve sevenths. To calculate, multiply the numerators (-4 and 9) to get -36, and the denominators (3 and 7) to get 21. Thus, the result is -36/21, which simplifies to -12/7.

Vol - 4096

Side - cube root of 4096

4096^(1/3) = 16 ( The side length).

Remember ' Csc(Cosecant)' = 1 /sin

Hence

Cos X 1/Sin = Cos/Sin = Cot (Cotangent)

Do NOT confuse with Tan = Sin /Cos. Notice the positions of trig. functions in the ratios.

Tan(0) = 0

Remember

Tan(0) = Sin(0)/Cos(0) = 0/1

And Sin(0) = 0

Hence it follows that Tan(0) = 0

1,414213562373095