an art student wants to make a string collage by connecting six equally spaced points on the circumference of a circle to its center with sting. What would be the radian measure of the angle between two adjacent pieces of string, in simplest form?

Well, as an art student, I'm sure your friend knows how to "string" it all together! But let me calculate the radian measure of the angle between two adjacent pieces of string for you.

To find this, we divide the full circumference of the circle (which is 2π radians) by the number of strings connecting the points. In this case, there are six strings connecting six equally spaced points. So, we divide 2π by 6:

2π / 6 = π / 3

So, the radian measure of the angle between two adjacent pieces of string would be π/3. But hey, even if your friend's art professor asks for a string collage, I hope they don't get tangled up in it themselves!

To find the radian measure of the angle between two adjacent pieces of string, we need to divide the circumference of the circle by the number of connecting points.

Step 1: Calculate the circumference of the circle:
The circumference of a circle is given by the formula C = 2πr, where r is the radius. Since the radius is not given, we can assume it as 1 for simplicity. Therefore, the circumference is C = 2π.

Step 2: Divide the circumference by the number of connecting points:
We have 6 equally spaced points on the circumference of the circle. So, we need to divide the circumference C by 6 to get the length of each string segment.
String length = C/6 = 2π/6 = π/3.

Step 3: Calculate the radian measure:
The radian measure is given by the formula θ = arc length / radius. Here, the arc length is the length of each string segment, which we calculated as π/3, and the radius is 1.
Therefore, the radian measure of the angle between two adjacent pieces of string is θ = (π/3) / 1 = π/3.

So, the radian measure of the angle between two adjacent pieces of string is π/3 in its simplest form.

To find the radian measure of the angle between two adjacent pieces of string, we need to consider the total angle formed at the center of the circle.

In this case, we have six equally spaced points on the circumference of the circle. The number of points on the circumference is equal to the number of angles formed at the center.

To determine the total angle, we divide the full circle (360 degrees or 2π radians) by the number of points on the circumference.

Step 1: Determine the total angle at the center
Total angle = 360 degrees / 6
Total angle = 60 degrees

Step 2: Convert to radians
To convert degrees to radians, we need to multiply by the conversion factor: π/180
Total angle in radians = 60 degrees * (π/180)
Total angle in radians = (π/3) radians

Step 3: Find the angle between two adjacent pieces of string
Since there are six equally spaced points, the angle between two adjacent pieces of string is simply the total angle divided by the number of points.
Angle between two adjacent pieces = (π/3) radians / 6
Angle between two adjacent pieces = π/18 radians

Therefore, the radian measure of the angle between two adjacent pieces of string is π/18 radians in simplest form.

Same answer

360 deg = circle

360/6 = 60 deg
60 deg * pi/360 = 60pi/360 = pi/3 rads