I tried posting this in Homework help but no one answered maybe i'll have better luck here?

Question

radian measure of the central angle of a circle of radius r that intercepts an arc length of s

Radius r = 1 meter

Arc length s = 600 centimeters


ty for helping

Answer 1

Usually one writes:

S = q*r where S= arc length, q = angle in radians, and r = radius of circle.

So you have S and r, then q = S/r = 600 cm/1m = 6 m/1m = 6 radians

Note a circle has 2*pi or about 6.28 radians so this is almost a full circle.

Answer 2

A radian is the angle which, when placed at the centre of a circle (or a sphere) will intercept the circle at two points separated by one radius.

So, if the circle has a radius of 1 metre, then a one radian angle placed at the centre of the circle will mark off an arc distance of 1 metre on the circle.

I will use 60 cm (not 600), but the principle is the same for any length.

60 cm is 0.6 m (there are 100 cm in 1 m). The length of the arc is simply proportional to the radius and to the angle.

1 radian gives us 1 m (= 100 cm) on the circumference, therefore
0.6 radian will give us 0.6 m (= 60 cm).

To find out the equivalent measure of the angle in degrees, then use the fact that an entire circle covers 360 degrees.
Also, the circumference of the circle is 2*pi*R where R is the radius.

Since the radian corresponds to an arc of one R, and 360 degrees corresponds to the full circumference of 2*pi*R, then one radian = 360 degrees divided by 2*pi.
one radian = 360/(2*pi) = 57.29577951... degrees.
0.6 radian = 0.6 * 57.29577951... = 34.377468... deg.

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If you really meant 600 cm (= 6 m) then the angle is 6 radians (343.77468... degrees).

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An angle of one radian at the centre gives an arc of one radius on the circumference. This feature makes the radian a "natural" unit to be used in advanced math.

In navigation and astronomy, where the degree has been used for thousands of years, there are also distance units that are created from angles at the centre of Earth and projected to the surface of the sphere:

(For this, you yave to imagine that the Earth is a sphere):
one minute (1/60 of a degree) gives an arc that measures one nautical mile. Therefore the circumference is 360*60 = 21,600 nautical miles.

In the metric system, there is an angle unit called the grade. 100 grades in a right angle and 400 grades in a full circle. Each grade is divided into 100 smaller parts, called centigrades.

One centigrade at Earth's centre gives an arc of 1 kilometre on the surface. Earth's circumference is therefore 400*100 = 40,000 km.

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In the modern international system of units, both have been redefined in terms of the new metre, which is based on the speed of light.

Answer 3

The answer is 6 radians, the very definition of a radian is 1 radian creates an arc length equal to the radius of the circle, so if the arc length is 6 x the radius, the angle will be 6 radians

Answer 4

The arc length is:
s = (angle in radians) * r

Plug in your values, convert your length units so they match, and calculate:
angle = 6 radians

Answer 5

Circum. of Cir. = 2 π r
Circum. of Cir. = 2 π (1)
Circum. of Cir. = 2 π
Circum. of Cir. = 6∙283 185 307... m = 360°

Arc S = 600cm = 6m

2 π r = 6∙283 185 307... m (÷ 2π)
r = 1 m (x 6)
6r = 6m