May someone please explain how to fill out the table ?
Question
Answer:
You have the formula written above the table.[tex] \theta = \dfrac{s}{r} [/tex]
where
[tex] \theta = measure ~of ~central ~angle ~in ~radians [/tex]
s = arc length
r = radius
The third lines of both tables need the angle. Since the formula is already solved for theta, the central angle, just plug in s and r and calculate theta.
Left table, third line
[tex] \theta = \dfrac{s}{r} = \dfrac{8 ~in.}{6~in.} = \dfrac{4}{3} [/tex]
Right table, third line
[tex] \theta = \dfrac{s}{r} = \dfrac{5~in.}{8~in.} = \dfrac{5}{8} [/tex]
For the first line of both tables, you are looking for the arc length. Solve the formula for s, arc length.
[tex] \theta = \dfrac{s}{r} [/tex]
[tex] s = \theta r [/tex]
Left table, first line
You have the radius, r = 8 in., and theta, but theta is in degrees. We need theta in radians.
[tex] \theta = 270^\circ \times \dfrac{\pi ~rad}{180^\circ} [/tex]
[tex] \theta = \dfrac{3 \pi}{2} ~ rad [/tex]
[tex] s = \theta r = \dfrac{3 \pi}{2} \times 8 in. = 12 \pi ~in. [/tex]
(You're correct.)
Right table, first line
[tex] s = \theta r = \dfrac{2 \pi}{3} \times 3 ~cm = 2 \pi ~cm [/tex]
For the second line of both tables, you are solving for the radius. We now solve the formula for r.
[tex] \theta = \dfrac{s}{r} [/tex]
[tex] r \theta = s [/tex]
[tex] r = \dfrac{s}{\theta} [/tex]
Left table, second line
[tex] r = \dfrac{s}{\theta} = \dfrac{1.5 ~cm}{1.05} = \dfrac{10}{7} ~cm [/tex]
Right table, second line
[tex] r = \dfrac{s}{\theta} = \dfrac{9 ~cm}{5} = \dfrac{9}{5} ~cm = 1.8 ~cm [/tex]
solved
general
11 months ago
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