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# C2 radians - arc length related question watch

1. Normal arc length equation is l=r?, but what about when the angle is a reflex (surpasses the 180° mark)?

Just needed for clarification as my C2 textbook says that its l=2? and I think this is wrong/am unsure about it, would have expected a r somewhere there.

Edit ~ the ? symbol should be theta, the forum doesn't seem to accept its presence.
2. It could be a wrong answer, very unlikely.
3. (Original post by snow leopard)
Normal arc length equation is l=r?, but what about when the angle is a reflex (surpasses the 180° mark)?

Just needed for clarification as my C2 textbook says that its l=2? and I think this is wrong/am unsure about it, would have expected a r somewhere there.

Edit ~ the ? symbol should be theta, the forum doesn't seem to accept its presence.
Arc length is r. It doesn't matter what the angle is as long as it's measured in radians.
4. Yeah, what gemini 92 said. Think about if you had a full circle, so theta would be 2pi. S = R*theta = 2R*pi, which you know is the circumference of a circle.
5. (Original post by Gemini92)
Arc length is r. It doesn't matter what the angle is as long as it's measured in radians.
The C2 2008 textbook edition would disagree if you check page 91 of Chapter 6 Part 6.2 Example 6.

When a reflex angle is involved it's different, but am dubious about a possible mistake in the equation as there is no mentioning of r.
6. (Original post by Jesse_Mac)
Yeah, what gemini 92 said. Think about if you had a full circle, so theta would be 2pi. S = R*theta = 2R*pi, which you know is the circumference of a circle.
The equation quoted by Gemini92 can only be applied to sectors of circles, which by definition cannot be bigger than 180°. I need to know the arc length equation for, hence, reflex angles.
7. The arc length is where theta is the angle subtended by the arc at the centre of the circle. End of story. Doesn't matter if it's acute, obtuse, or reflex.

The only other equation you might see, is when you know one angle and want the arc length corresponding to the complementary angle, in which case you might see
8. (Original post by ghostwalker)
The arc length is where theta is the angle subtended by the arc at the centre of the circle. End of story. Doesn't matter if it's acute, obtuse, or reflex.

The only other equation you might see, is when you know one angle and want the arc length of the angle subtended by the complementary angle, in which case you might see
That's what I was looking for, thanks. /thread
9. (Original post by snow leopard)
x (surpasses the 180° mark)?

10. Yeah, the length of the arc is always r theta, even when the angle is reflex. If you are trying to find the length of a major arc, and you're given the angle of the minor arc, the reflex angle is equal to (2pi - theta), so the length is r(2pi - theta). Perhaps this is where you are getting confused.

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