Question

Determine the following : a) what is the angle formed by an arc length of 3 radii?

b) what is the angle formed by an arc length of 1 radii?

c) what is the angle formed by an arc length of pi/2 radii?

d) what is the angle formed by an arc length of 4pi/3 radii?

Answer 1

Length of the arc = r * , where r is the radius and is the angle in radians

To convert radians into degrees, we need to multiply the degrees value by

I have given both values in degrees and in radians for your reference.

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(a) Arc length = 3r

Therefore 3r = r * ,

= 3 radians

For degrees, = 3 * 180/ = 540/ degrees

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(b) Arc length = 1r

Therefore 1r = r * ,

= 1 radians

For degrees, = 1 * 180/ = 180/ degrees

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(c) Arc length = (/2) r

Therefore (/2) r = r * ,

= /2 radians

For degrees, = (/2) * 180/ = 90 degrees

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(d) Arc length = (4/3) r

Therefore (4/3) r = r * ,

= 4/3 radians

For degrees, = (4/3) * 180/ = 240 degrees

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