Question

Drag each number to the correct location on the calculation and statement. Each number can be used more than once, but not all numbers will be used.

Complete the calculation and statement about the radian measure of angle θ, as well as the arc that subtends it, both shown on the unit circle above.


Arc length = 1/8 * _____ * r
= ____ * r
= π/4 * ____
= ____ units

The radian measure of an angle is equal to the length of the corresponding arc on the unit circle. Therefore, angle θ has a measure of ___ radians

Options to fill in blanks:
2π
1
π/4
π/2
2π/3
π/6
π

Answer 1

Explanation:

Arc length of a circle is given by,

Arc length =
`(\theta)/(360)(2\pi r)`

Here, θ = Central angle subtended by the arc

r = Radius of the circle

From the given picture,

θ = 45°

r = 1 unit

Therefore, arc length =
`(45)/(360)(2\pi r)`

=
`(1)/(8)(2\pi r)`

=
`(2\pi )/(8)(r)`

=
`(\pi)/(4)(r)`

Arc length =
`(\pi)/(4)(1)` units

=
`(\pi )/(4)` units

Angle θ has a measure =
`(45)/(360)* \pi`

=
`(\pi)/(8)` radians