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radians

i dont understand them can anyone help me

What don't you understand about them? They are a unit for measuring angles.

There are

2\pi

radians in a circle. And 1 radian is equal to

\frac{180}{\pi}

degrees.

Reply 2

Mohit_C

To covert from degrees to radians, you multiply by pi and divide by 180. If you convert from radians to degrees, you multiply by 180 and divide by pi. Simple as that.

Reply 3

Morbo

whopper112

i dont understand them can anyone help me

Like jppowell says.

Imagine cutting up a pie such that the length of the curved crust of the slice is the same as the radius of the pie. The angle that the slice subtends at the centre of the pie is defined as 1 radian.

Since the circumference of a circle is

2\pi r

, there are therefore

2\pi

radians in a full circle.

Reply 4

BibbleJW

As Worzo said, a radian is the angle where a piece od the circle has the same length on all sides (2 lots of the radius, and a radius length for the arc). The theory behind it is that it is a measure of the angle of an arc, with respect to the length of the curve and the radius of the circle.
I find the best was to remember the figures involved is that the formula for the circumference is 2pi(r). So there are 2pi radians in a circle.

Reply 5

jpowell

The reason we use radians in mathematics, is that they are the natural unit for working with the trigonometric functions. If you used the trigonometric functions with a unit other than radians then the derivative of sin would not be cos, but some factor multiplied by cos. With radians the factor is 1, and hence makes calculus and trigonometry simpler.

Reply 6

Sidhe

I'm using them in matrix transformations at the moment for example.

sin (\frac{pi}{4})

radians can be easilly converted into a surd such as

sin (\frac{\pi}{4})=\sqrt {2}

for example which makes matrix multiplication a lot easier than using degrees or cumbersome numbers such as

0.785398163=sin (\frac {\pi}{4})

radians. You can use trigonometry to work out all the surds of sin cos tan, ie pythagoras theorem so with a bit of practice they become nice convenient alternatives.

create a right angled triangle with one of the
angles being the one you want. So as pi/3=60 degrees we have an
equilateral triangle, split it down the middle and call the original side
length 2.

Sin=opposite/hypotenuse

This gives a right angled triangle opposite 1, hypotenuse= 2,

\sqrt {3}

so sin pi/3 will
be

\frac{opposite}{hypotenuse}=\sqrt{\frac{3}{2}}

. Similar with 1,1, hypotenuse

\sqrt {2}

will give you

\frac {\pi}{4}

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