# Converting Trigonometric Ratios to Degree

1. May 10, 2012

Hi! I'm just a beginner i don't know much about trigonometry... can you tell me how to convert the trigonometric ratios to degree.. for example:
o.3333 how did it become 19.47degree ? i saw it in the book... can you tell me how? I know this is simple for you all!!! i want to solve it without using calculator... is there a formula to solve it manually?

Last edited: May 10, 2012
2. May 10, 2012

### scurty

Yes, there is a formula! The formula is simply a ratio. This isn't just used in math, it is used in physics and chemistry all the time to change units of measure (which is the same thing we are doing here).

How many radians are in a circle? $2 \pi$ rad
How many degree are in a circle? $360^{\circ}$

Therefore, $2 \pi \text{ rad} = 360^{\circ}$

And so, $1 = \frac{2 \pi \text{ rad}}{360^{\circ}} = \frac{360^{\circ}}{2 \pi \text{ rad}}$.

So, in your example, you have $0.3333 \text{ rad}$. Multiply by one so that the radians cancel with radians.

$0.3333 \text{ rad} \cdot 1 = 0.3333 \text{ rad} \cdot \frac{360^{\circ}}{2 \pi \text{ rad}} \approx 19.1^{\circ}$

I'm not sure how the book got 19.47 degrees, they are off by a bit.

I hope that clears it up!