Converting Trigonometric Ratios to Degree

In summary, to convert a trigonometric ratio to degrees, you can use the formula ##1 = \frac{2 \pi \text{ rad}}{360^{\circ}}##. To convert 0.3333 radians to degrees, you can multiply it by 360 degrees and then divide by 2pi radians, which gives a result of approximately 19.1 degrees.
  • #1
ahmadaming60
1
0
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:
Physics news on Phys.org
  • #2
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!
 

What is a trigonometric ratio?

A trigonometric ratio is a mathematical relationship between the sides of a right triangle and its angles. It is used to solve for unknown side lengths or angles in a triangle.

How do you convert a trigonometric ratio to degrees?

To convert a trigonometric ratio to degrees, you can use the inverse trigonometric functions. For example, to convert sine to degrees, you would use the arcsine function on a calculator or use a trigonometric table to find the corresponding angle.

What are the common trigonometric ratios?

The most common trigonometric ratios are sine, cosine, and tangent. These ratios are used to represent the relationship between the opposite, adjacent, and hypotenuse sides of a right triangle.

Why is it important to convert trigonometric ratios to degrees?

Converting trigonometric ratios to degrees is important because it allows us to work with angles in a more familiar unit of measurement. Degrees are commonly used in everyday life, whereas radians (the unit of measurement for trigonometric ratios) are more commonly used in mathematics and science.

Are there any shortcuts for converting trigonometric ratios to degrees?

Yes, there are a few shortcuts that can be used to quickly convert trigonometric ratios to degrees. For example, you can use the “SOH-CAH-TOA” acronym to remember the ratios for sine, cosine, and tangent. Also, memorizing common angles and their corresponding trigonometric ratios can make the conversion process faster.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
14
Views
745
Replies
5
Views
2K
Replies
3
Views
1K
  • Calculus
Replies
5
Views
1K
Replies
3
Views
1K
Replies
1
Views
2K
  • Calculus and Beyond Homework Help
Replies
30
Views
2K
  • Precalculus Mathematics Homework Help
Replies
10
Views
1K
Back
Top