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Consider the diagram shown. Choose all the true statements.

If Θ = 2 rad, then r > s.

If Θ = 1 rad, then r ≤ s.

If s = 1/2r, then 2Θ = 1.

If s/2r=1, then Θ = 2

Consider the diagram shown Choose all the true statements If Θ 2 rad then r gt s If Θ 1 rad then r s If s 12r then 2Θ 1 If s2r1 then Θ 2 class=

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Answer:

If Θ = 1 rad, then r ≤ s

If s = 1/2r, then 2Θ = 1

If s/(2r)=1, then Θ = 2

Step-by-step explanation:

we know that

The arc length s is equal to

[tex]s=r\theta[/tex]

where

r is the radius

[tex]\theta[/tex] is the central angle in radians

Verify each statement

case 1) If Θ = 2 rad, then r > s

The statement is false

Because

For Θ = 2 rad

substitute

[tex]s=r(2)\\s=2r[/tex]

so

[tex]s>r[/tex]

case 2) If Θ = 1 rad, then r ≤ s

The statement is true

Because

For Θ = 1 rad

substitute

[tex]s=r(1)[/tex]

[tex]s=r[/tex]

so

[tex]r\leq s[/tex] ---> is true

case 3) If s = 1/2r, then 2Θ = 1

The statement is true

Because

For s=1/2r

substitute

[tex]\frac{1}{2}r=r\theta[/tex]

[tex]\theta=\frac{1}{2}[/tex]

[tex]2\theta=1[/tex]

case 4) If s/2r=1, then Θ = 2

The statement is true

Because

For Θ = 2

substitute

[tex]s=r(2)\\\\\frac{s}{2r}=1[/tex]

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