Question

1) A designer takes an arc n times and rotates it anti-clockwise about a centre C, which sits at the origin of

a graph (0,0).

The arc looks like this.

The number of arcs, n, and the Angle of rotation is found in the table.

Note that Angle forms a number sequence of 0^o, 90^o, and 180^o, ...

Fill in the missing values in the table below.

n	Angles (in degrees)
1	0
2	90
3	180

Based on question 1, how does n increase?   Write a formula for:

n = _______________

Based on question 1, find a formula to calculate the rotation Angle for each arc (Hint: observe the differences in each Angle to determine an appropriate number sequence rule). Note that n is the variable.

Angle = _____________ n - ________________

Answer 1

We have given in the question that

for n=1, Rotation Angle=0o; for n=2, Angle=90o; for n=3, Angle=180o and so on

Where n=no. of arcs

Rotation Angles form a number sequence of 0o, 90o​​ ​​​​, 180o,...

So from the above data, we can deduce for a given angle no. of arc will be

Also for the rotation angle, we can rearrange the above equation, which gives us

So we can calculate rotation angle for given number of arcs and vice versa.