I Can the same argument be used for both radians and degrees in the sine function?

[fog37]

TL;DR Summary

angle argument of a sine function

Hello,
I understand that the sine function take an argument as an input and produced an output which is a real number between 1 and -1. My question is about the argument. I know it can be in either radians or degrees which are different units to measure angle. An angle is the portion of the plane between two lines that meet at a vertex.

For example, let's consider a function that takes the length of the side as input and calculates the perimeter of a square: $f(x)=4x$. The output is correct regardless of the input being in feet, meter, inches, etc. However, the numerical output is different depending on the unit of $x$.

What about in the case of the function $f(x)=sin(x)$ or $f(x)=3sin(4x+30^\circ)$? If $x$ is in radians or degrees, the answer is the same...How is that possible? I am trying to explain this concept to a friend but I am convincing and clear.

thanks!

 

[FactChecker]

If those are interpreted by a human, he can make the appropriate adjustment in his interpretation. If they are in computer code, then the computer language will insist that the input to sin() is in radians. If you want to use degrees, you will need to make the appropriate conversion of units: sin( degToRad * x_degrees), where degToRad = $\pi / 180 = 0.0174532925199433$.
It is very common to see a mistake in computer programs where the input to the sin() function is degrees without the conversion. The effects are serious. A tiny change in degrees is interpreted as a change in radians, which is much larger.

 

[gmax137]

I'm not a mathematician, but I think the sine function works on radians, a dimensionless number (radian measure is a ratio). Your calculator uses the Taylor series (or some other faster series:

sin(x) = x+ x^3/3! - x^5/5! ...

If your calculator takes the argument in degrees, it first converts to radians (rad = pi * (deg/180)).

EDIT: basically, what @FactChecker just said.

 

[PeroK]

TL;DR Summary: angle argument of a sine function

Hello,
I understand that the sine function take an argument as an input and produced an output which is a real number between 1 and -1. My question is about the argument. I know it can be in either radians or degrees which are different units to measure angle. An angle is the portion of the plane between two lines that meet at a vertex.

For example, let's consider a function that takes the length of the side as input and calculates the perimeter of a square: $f(x)=4x$. The output is correct regardless of the input being in feet, meter, inches, etc. However, the numerical output is different depending on the unit of $x$.

What about in the case of the function $f(x)=sin(x)$ or $f(x)=3sin(4x+30^\circ)$? If $x$ is in radians or degrees, the answer is the same...How is that possible? I am trying to explain this concept to a friend but I am convincing and clear.

thanks!

The sine function in general mathematics is almost always has an argument in radians. That said, using degrees is quite common in engineering and mechanics problems.