Converting radians to degrees

How do you convert radians into degrees, and then degrees back to radians again? So confused!!

To convert radians into degrees:
Multiply by 180 then divide by pi or multiply by 180/pi

To convert degrees into radians:
Multiply by pi then divide by 180 or multiply by pi/180

Reply 2

Tillybop

Thank you so much :smile:

No problem :biggrin:

Pi is the number defined by the ratio of: Circumference to Diameter.
Thus:

\pi= C/2r

Proof 2Pi radians in a circle

\pi= C/2r \Rightarrow 2\pi r = C \Rightarrow

\frac{C} {k}=(\frac {2\pi} {k}) r

This means that for any angle,

\theta,

such that

\theta= \frac{2 \pi} { k}

,
we have derived the formula relating the sector length to the angle inscribed in that sector (

l= r \theta

). This shows there are, indeed, 2pi radians in a circle, for it is only when theta is 2pi that the length of the sector is the same as the circumference.
How to convert from radians into degrees and vice versa
Suppose theta in degrees and alpha in radians are the same angle. We therefore have the direct relationship

\alpha*360= \theta*2\pi

. To find alpha or theta, we just rearrange to make either alpha or beta the subject of the above.

Reply 5

Bow Tie

Easiest way I remember is that there is 180 degrees in a pi radian (or in a circle (360 degrees) there are 2pi radians).

From there you can go places...