B Radians vs Degrees: Math Trigonometry Explained

[johann1301h]

Im teaching math and one of my students asked me something about trigonometry.

Say you are to generally solve:

sin(x + 1) = 0.5

And that's all the information you are given.

How would you know to solve for radians or degrees?

 

[fresh_42]

You don't. It's probably decided by the context: in mathematics alone I would always chose radians, but in a conversation with ordinary people, degrees might be a better choice. It's the same as with any units, take the appropriate ones in the context.

 

[Svein]

Im teaching math and one of my students asked me something about trigonometry.

Say you are to generally solve:

sin(x + 1) = 0.5

And that's all the information you are given.

How would you know to solve for radians or degrees?

If the problem is given as shown, the answer must be in radians. If degrees were meant, the problem should have been stated

sin(x + 1°) = 0.5

 

[mfb]

If the problem is given as shown, the answer must be in radians. If degrees were meant, the problem should have been stated

sin(x + 1°) = 0.5

That's what I thought as well. "1" without degree sign means we are working with radians, otherwise adding 1 doesn't make sense. If the question is sin(2*x)=0.5 then we cannot tell.

 

[Svein]

That's what I thought as well. "1" without degree sign means we are working with radians, otherwise adding 1 doesn't make sense. If the question is sin(2*x)=0.5 then we cannot tell.

Then you indicate what type of answer you have given, such as x = 15° or x = π/12.

 

[malemdk]

Generally it is degree.

 

[jbriggs444]

Generally it is degree.

Not if your degree is in mathematics.

 

[Mark44]

Generally it is degree.

Not if your degree is in mathematics.

The use of radians is much more prevalent in mathematics, especially at the level of calculus and above. All of the differentiation and integration formulas for the trig functions use radians exclusively.