# 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

## The Attempt at a Solution

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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

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