Help with Radians: Find Angles in Radians

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In summary, we discussed how to convert from degrees to radians and found that 1 degree is equal to π/180 radians. We then solved for the angle θ = 249 degrees, which is equivalent to 83π/60 radians or approximately 4.35 radians. We also learned about different notations for radians, such as using the superscript c or R.
  • #1
tenchick19
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I need help with radians.. One of my questions is: An angle of 0 (with line through it) =249 degrees is equivalent to how many radians? Answer in units of rad.
Thanks!
 
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  • #2
1 degree = [itex]\pi[/itex]/180 radians. Angle [itex]\theta[/itex] = 249 degrees. What do you think you should do?
 
  • #3
Would the answer be 4.35 radians?
 
  • #4
tenchick19 said:
Would the answer be 4.35 radians?
Yes, but that would be an approximation.

[tex]249^\circ = \frac{{249\pi }}{{180}}rad = \frac{{83\pi }}{{60}}rad \approx 4.35rad[/tex]
 
  • #5
That's what I get, if you're rounding.

I forgot you got to be fast around here. :biggrin:
 
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  • #6
thank you so much!
 
  • #7
honestrosewater said:
That's what I get, if you're rounding.

I forgot you got to be fast around here. :biggrin:
:blushing:

tenchick19 said:
thank you so much!
Glad we could help :smile:
 
  • #8
Just a really, really, really small point. Radians, I am sure, can be written as [tex]\pi ^c[/tex].

Like I said - a really, realy, really small point.

The Bob (2004 ©)
 
  • #9
The Bob said:
Just a really, really, really small point. Radians, I am sure, can be written as [tex]\pi ^c[/tex].

Like I said - a really, realy, really small point.

The Bob (2004 ©)

I never knew that, in my books, they always denoted radians by putting a little R superscript, like so:

[itex]2\pi^R[/itex]
 
  • #10
FluxCapacitator said:
I never knew that, in my books, they always denoted radians by putting a little R superscript, like so:

[itex]2\pi^R[/itex]
Really? I usually use c. I have never seen that before. I expected to R when I studied radians but we use c.

The Bob (2004 ©)
 

What is a radian?

A radian is a unit of measurement for angles, symbolized by "rad". It is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. One radian is approximately equal to 57.3 degrees.

How do I convert degrees to radians?

To convert degrees to radians, you can use the formula: radians = (degrees * pi) / 180. Alternatively, you can also use a calculator that has a radians function.

How do I find the reference angle in radians?

The reference angle in radians is the smallest positive angle that can be formed by rotating the terminal side of an angle in standard position onto the x-axis. To find the reference angle in radians, you can use the formula: reference angle = angle - (n * 2pi), where n is the number of revolutions the angle makes around the origin.

What is the difference between radians and degrees?

Radians and degrees are two different units of measurement for angles. While degrees are based on dividing a circle into 360 equal parts, radians are based on the ratio of the length of an arc to the radius of a circle. Radians are often used in higher level mathematics and physics, while degrees are more commonly used in everyday measurements.

How can I use radians to find the length of an arc?

To find the length of an arc in radians, you can use the formula: arc length = radius * angle. This formula works because the arc length is proportional to the radius and the angle in radians.

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