# How do you tell if tan x=0.5371, is in radian or degree?

## Homework Statement

How do you tell if tan x=0.5371, (0.5371)is in radian or degree? ($$0\leq$$$$x\leq$$$$2\pi$$)

thanks

## Answers and Replies

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Pengwuino
Gold Member
0.5371 is just a number. The argument, x, of tan(x), however, could be in radians or degrees.

Is that mean, there will be two answer for this?
In degree mode, i got 28.24 degree
radian: 0.492885...degree?

Last edited:
Pengwuino
Gold Member
You asked if tan(x) = 0.5371, then is 0.5371 is in radians or degree? It is neither, 0.5371 is a dimensionless number.

Now, if you're asking whether or not X is in radians or degrees and what is it's value? Then the answer to that is there are 2 values of X that produce that result (~28 degrees and ~208 degrees) and X can be in radians OR degrees. Since you're typically making calculations on a calculator or computer, the device will want it in degrees or radians and you should be able to determine this. If it's in radians, instead of say 90 degrees, you'd enter it as $$\frac{\pi}{2}$$ which is roughly 1.5708 radians.

You asked if tan(x) = 0.5371, then is 0.5371 is in radians or degree? It is neither, 0.5371 is a dimensionless number.

Now, if you're asking whether or not X is in radians or degrees and what is it's value? Then the answer to that is there are 2 values of X that produce that result (~28 degrees and ~208 degrees) and X can be in radians OR degrees. Since you're typically making calculations on a calculator or computer, the device will want it in degrees or radians and you should be able to determine this. If it's in radians, instead of say 90 degrees, you'd enter it as $$\frac{\pi}{2}$$ which is roughly 1.5708 radians.
Oh, I was confused on something, that's why..
Thanks...

my trig teacher told me that a number is in radians if there is no unit after it. degrees however is not unitless

i assume your answer should be in radians and therefore you should use the degree mode on your calculator. if im wrong, you can easily convert from radians to degrees by multiplying your answer by 180 over pi,. although it might be even easier to just switch to degrees on the calculators./yes

HallsofIvy
Science Advisor
Homework Helper
my trig teacher told me that a number is in radians if there is no unit after it. degrees however is not unitless
That's not a mathematical "law" but it is a pretty widely used convention. You might also say that if a problem just treats trig functions "as functions" with no angles or triangles involved, then you should think of the argument as being in radians. Degrees are used almost exclusively for "angle" problems while sine and cosine are used for much more.

i assume your answer should be in radians and therefore you should use the degree mode on your calculator. if im wrong,
Surely that's not what you meant to say! If your answer should be in radians then you should use radian mode!

you can easily convert from radians to degrees by multiplying your answer by 180 over pi,. although it might be even easier to just switch to degrees on the calculators./yes