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Radians and Arc Length (Radians)Radians and Arc Length (Radians)
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Question 1 of 4
1. Question
Find the value of `theta`
- `theta=` (1)
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Arc Length Formula
`l``=``r``theta`Substitute the known values and solve for `theta``l` `=` `8` `r` `=` `8` `l` `=` `r``theta` `8` `=` `8``theta` Substitute known values `8``divide8` `=` `8theta``divide8` Divide both sides by `8` `1` `=` `theta` `theta` `=` `1` `theta=1` -
Question 2 of 4
2. Question
Find the value of `theta`
- `theta=` (1.8)
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Arc Length Formula
`l``=``r``theta`Substitute the known values and solve for `theta``l` `=` `9` `r` `=` `5` `l` `=` `r``theta` `9` `=` `5``theta` Substitute known values `9``divide5` `=` `5theta``divide5` Divide both sides by `5` `1.8` `=` `theta` `theta` `=` `1.8` `theta=1.8` -
Question 3 of 4
3. Question
Find the value of `theta`
Use `pi=3.14`- `theta=` (1.88)
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Arc Length Formula
`l``=``r``theta`First, substitute the known values and solve for angle of the shaded region`l` `=` `44` `r` `=` `10` `l` `=` `r``theta` `44` `=` `10``theta` Substitute known values `44``divide10` `=` `10theta``divide10` Divide both sides by `10` `4.4` `=` `theta` `theta` `=` `4.4` Angle of the shaded region Finally, subtract the angle of the shaded region from the total angle of a circle `(2pi)` to get the value of `theta``2pi-``4.4` `=` `(2xx3.14)-4.4` `=` `6.28-4.4` `=` `1.88` `theta=1.88` -
Question 4 of 4
4. Question
Given that `A=300\text(cm)^2`, find the value of `theta` in degrees
Use `pi=3.1415`
Round your answer to one decimal place- `theta=` (14.7)`°`
Hint
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Arc Length Formula
`l``=``r``theta`Area of a Circle Formula
$$A=\pi\color{#9a00c7}{r}^2$$Converting Radian to Degrees
`\text(degrees)=\text(radian)xx(180°)/pi`First, use the area of a circle formula and solve for `r``\text(Area)` `=` `300` `\text(Area)` `=` $$\pi\color{#9a00c7}{r}^2$$ `300` `=` $$\pi\color{#9a00c7}{r}^2$$ Substitute known values `300``divide pi` `=` `pi r^2``divide pi` Divide both sides by `pi` `sqrt(300/(pi))` `=` `sqrt(r^2)` Find the square root of both sides `9.772` `=` `r` `r` `=` `9.772` Next, substitute the known values and solve for `theta``l` `=` `2.5` `r` `=` `9.772` `l` `=` `r``theta` `2.5` `=` `9.772``theta` Substitute known values `2.5``divide9.772` `=` `9.772theta``divide9.772` Divide both sides by `9.772` `0.2558` `=` `theta` `theta` `=` `0.2558` Finally, convert the radian to degrees`\text(degrees)` `=` `\text(radians)xx(180°)/pi` `=` `0.2558xx(180°)/pi` `=` `(46.044°)/(3.1415)` Use `pi=3.1415` `=` `14.7°` Rounded to one decimal place `theta=14.7°`