Would arctan(y/x) give you angle in radian?

[Endercreeper01]

Would the arctangent of y/x give you the angle in radians?

[Unity+]

What do you mean "give you the angle in radians"? And what do you mean in context of y/x? Please explain what you are trying to do.

[Endercreeper01]

When you use the definition of the trig functions with the right triangle, then you have:

 

tan(a)=y/x

 

Where a is the angle, y is the opposite, and x is the adjacent side.

If you go by this definition of the trig functions, and you do arctan(y/x), would you get a in radians?

[Unity+]

It would depend on what setting you are using on a calculator(if you are just using a calculator to calculate the tangent).

 

If the calculator is set in radians then it will output the value in radians. If it is set to degrees then the output will be degrees. This is if I understand the question correctly.

[Endercreeper01]

I mean if you use the triangle definition for a tangent and insert that into the equation for an angle based on tangent and arctangent

Edited November 23, 2013 by Endercreeper01

[Unity+]

I mean if you use the triangle definition for a tangent and insert that into the equation for an angle based on tangent and arctangent

Wait...you are beginning to confuse me....

 

What do you mean by triangle definition? Tangent has only one definition. It is context that is needed. For example, there is something called the tangent of a circle. However, you are referring to the context of a triangle. There is only one definition of tangent. It is where it is applied that changes everything.

 

Again, based on the information, it depends on whether the calculator your using is set to radians or degrees. I am still confused on what the question is, if this isn't the answer to the right question. Could someone else help me here?

[John Cuthber]

 

 

Tangent has only one definition

It has several.

http://www.oxforddictionaries.com/definition/english/tangent

I don't think the one which is related to arctan is a line with the same gradient that touches a curve or an abrupt change of subject.

[Unity+]

It has several.

http://www.oxforddictionaries.com/definition/english/tangent

I don't think the one which is related to arctan is a line with the same gradient that touches a curve or an abrupt change of subject.

It was merely an example. And, the other definitions merely differ based on context. It is like having different sub classes in a class. The subclasses may be different contexts, but still lie in the same class.

 

• a straight line or plane that touches a curve or curved surface at a point, but if extended does not cross it at that point.
• a completely different line of thought or action
• Mathematics the trigonometric function that is equal to the ratio of the sides (other than the hypotenuse) opposite and adjacent to an angle in a right-angled triangle

They all deal with, in one way or another, a line that either touches a curve or (whatever).

 

They involve one concept, but can be applied to many contexts, if you understand what I am saying.

[Endercreeper01]

I mean the definition where you have the tangent as opposite divided by adjacent

Edited November 23, 2013 by Endercreeper01

[John Cuthber]

Here's an angle

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you can split it into two right angled triangles by drawing a horizontal line through the middle of it.

You can then calculate the opposite over the adjacent and you will get an answer something like 0.5

 

So the tangent of that angle (between one of those lines and the horizontal) is about 0.5

 

So far I have not mentioned any units.

If someone told you that the arctan of an angle was 0.5 you could draw the angle.

and then you could measure that angle in any units you liked- degrees, radians, grads whatever.

 

Your calculator can't draw an angle for you as a reply to the question "what is arctan 0.5?" It has to give you a number.

And that number will depend on whether you have set the calculator to deal in radians degreed grads or whatever.

[Olinguito]

Would the arctangent of y/x give you the angle in radians?

It can be in any angular unit you like radians, degrees, grads, anything. You simply set your calculator to the angular unit you want and compute the inverse tangent.

 

Note however that in some cases you have to use only radians. For example, if [latex]f(t)=\arctan t[/latex] and you compute [latex]f'(t)=\frac1{1+t^2}[/latex], then in order for the formula to work, [latex]t[/latex] must be in radians. You have to be aware of cases when you must use radians; otherwise you have a choice of radians or degrees.