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Homework Statement
How do you tell if tan x=0.5371, (0.5371)is in radian or degree? ([tex]0\leq[/tex][tex]x\leq[/tex][tex]2\pi[/tex])thanks
Pengwuino said: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 [tex]\frac{\pi}{2}[/tex] which is roughly 1.5708 radians.
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.sportsstar469 said:my trig teacher told me that a number is in radians if there is no unit after it. degrees however is not unitless
Surely that's not what you meant to say! If your answer should be in radians then you should use radian mode!i assume your answer should be in radians and therefore you should use the degree mode on your calculator. if I am 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
To convert from radians to degrees, use the formula degrees = radians * (180/π). In this case, degrees = 0.5371 * (180/π) ≈ 30.79°. Therefore, tan x=0.5371 is approximately equal to 30.79°.
To convert from degrees to radians, use the formula radians = degrees * (π/180). In this case, radians = 0.5371 * (π/180) ≈ 0.00938 radians. Therefore, tan x=0.5371 is approximately equal to 0.00938 radians.
Tan x=0.5371 is a trigonometric function, which can be expressed in both radians and degrees. To determine which unit it is in, you can look at the context of the problem or the units of other trigonometric functions in the same equation. If the other functions are in degrees, then tan x=0.5371 is also likely in degrees. If the other functions are in radians, then tan x=0.5371 is likely in radians. You can also use a calculator to check the result in both units and see which one matches the given value.
Radians and degrees are units of measurement used to express angles. Radians are based on the radius of a circle, where 2π radians is equal to 360 degrees. Degrees, on the other hand, are based on dividing a circle into 360 equal parts. Radians are commonly used in calculus and higher level mathematics, while degrees are used more in everyday life and basic geometry.
Yes, most scientific calculators have a function to convert between radians and degrees. Look for a "deg/rad" or "mode" button on your calculator and switch to the desired unit before entering the value for tan x=0.5371. This will give you the converted value for tan x=0.5371 in the unit you selected.