Hello!
What does this mean?
...find the lenght of the arc subtended by an angle of measure 2...
(I suck at English :) )
3 answers
It means, on a circle, find the length of the arc at the end of a radius, rotated through some angle. Of course, you know the length if it is a complete circle as 2PI*radius.
If you draw two radii of a circle with center O, and they intersect the circle at A and B, then angle AOB is said to subtend the arc AB.
The length of the circular arc AB is rθ, where θ is measured in radians.
An angle of π/2 is a right angle, so it subtends 1/4 of a circle. The whole circumference is 2πr, so πr/2 is 1/4 of that.
For your problem, an angle of measure 2 will subtend an arc of length 2r, whatever the radius r of the circle is.
The length of the circular arc AB is rθ, where θ is measured in radians.
An angle of π/2 is a right angle, so it subtends 1/4 of a circle. The whole circumference is 2πr, so πr/2 is 1/4 of that.
For your problem, an angle of measure 2 will subtend an arc of length 2r, whatever the radius r of the circle is.
Tahnk you very much!
2 answers