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Do you use radians or degrees for sin?
Radians. Most of the time we measure angles in degrees. For example, there are 360° in a full circle or one cycle of a sine wave, and sin(30°) = 0.5 and cos(90°) = 0. But it turns out that a more natural measure for angles, at least in mathematics, is in radians.
Are radians or degrees more accurate?
Mathematically, radians are more natural than degrees. To give a few examples, if you differentiate sin(x), where x is in radians, you get cos(x), but if x is in degrees, you get (pi/180)*cos(x).
What is the difference between radian and degree mode?
A radian is equal to 180 degrees because a whole circle is 360 degrees and is equal to two pi radians. A radian is not as widely used in the measurement of circles and angles as a degree because it involves the knowledge of higher mathematics and includes tangents, sine, and cosines which are taught in college.
When should you use radians?
You should use radians when you are looking at objects moving in circular paths or parts of circular path. In particular, rotational motion equations are almost always expressed using radians.
Why are radians needed?
Radians make it possible to relate a linear measure and an angle measure. A unit circle is a circle whose radius is one unit. The one unit radius is the same as one unit along the circumference.
What is the relationship between radian and degree?
It follows that the magnitude in radians of one complete revolution (360 degrees) is the length of the entire circumference divided by the radius, or 2πr / r, or 2π. Thus 2π radians is equal to 360 degrees, meaning that one radian is equal to 180/π ≈ 57.295779513082320876 degrees.
What is a rad in physics?
The radian is the Standard International (SI) unit of plane angular measure. The angle q, representing one radian, is such that the length of the subtended circular arc is equal to the radius, r, of the circle. The radian is used by mathematicians, physicists, and engineers.
Why do we use degrees instead of radians to measure sine?
Notice that when measured in radians sin (x)≈x for small x, and when using degrees sine is really stretched out. Clearly when using degrees the slope (derivative) of sine at zero is not 1, it’s much smaller (it’s 2 π /360 in fact). If you don’t want any weird extra constants, then you need to use radians.
What is the value of sin 2 radians equal to?
That is: 2 π radians = 360 degrees. You’ll notice that when the angle is very small (and measured in radians) the value of sin (θ) and the value of θ itself become very nearly equal. Not too surprisingly, this is called the “small angle approximation” and it’s remarkably useful.
Can radians take you places degrees can’t?
Still, when push comes to shove, radians can take you places that degrees simply can’t. That’s why, when my Trig students give an angle in degrees instead of radians, I tell them: “I’m sorry, I don’t speak Babylonian.”
What is the value of sin(θ) = 360 degrees?
The circumference of a circle or radius R is 2 π R, so (since R=1 on the unit circle) the full circle is 2 π radians around. That is: 2 π radians = 360 degrees. You’ll notice that when the angle is very small (and measured in radians) the value of sin (θ) and the value of θ itself become very nearly equal.