QUESTION IMAGE
Question
hw - jan 8 - converting radians to degrees maze
start
$\frac{pi}{18}$
$10^circ$
$-\frac{3pi}{2}$
$-10^circ$
$\frac{7pi}{3}$
$420^circ$
$\frac{7pi}{4}$
$20^circ$
$270^circ$
$-270^circ$
$135^circ$
$240^circ$
$-340^circ$
$315^circ$
$\frac{3pi}{4}$
$153^circ$
$\frac{pi}{3}$
$120^circ$
$-\frac{17pi}{9}$
$340^circ$
$-\frac{11pi}{6}$
$135^circ$
$60^circ$
$30^circ$
$180^circ$
$535^circ$
$340^circ$
$-330^circ$
$-\frac{11pi}{3}$
$-660^circ$
$-\frac{25pi}{12}$
$-375^circ$
$\frac{107pi}{36}$
$-535^circ$
finish!
https://unitedasd.schoology.com/common-assessment-delivery/start/8191227862?action=onresume&submissionid=1808933094
To solve the maze, we convert radians to degrees using the formula \( \text{Degrees} = \text{Radians} \times \frac{180^\circ}{\pi} \). Let's go step by step:
Step 1: Start with \( \frac{\pi}{18} \)
Using the conversion formula:
\( \frac{\pi}{18} \times \frac{180^\circ}{\pi} = \frac{180^\circ}{18} = 10^\circ \).
So we follow the \( 10^\circ \) arrow.
Step 2: Next, \( -\frac{3\pi}{2} \)
Convert to degrees:
\( -\frac{3\pi}{2} \times \frac{180^\circ}{\pi} = -3 \times 90^\circ = -270^\circ \).
Follow the \( -270^\circ \) arrow.
Step 3: Next, \( \frac{7\pi}{3} \)
Convert to degrees:
\( \frac{7\pi}{3} \times \frac{180^\circ}{\pi} = 7 \times 60^\circ = 420^\circ \).
Follow the \( 420^\circ \) arrow.
Step 4: Next, \( \frac{7\pi}{4} \)
Convert to degrees:
\( \frac{7\pi}{4} \times \frac{180^\circ}{\pi} = 7 \times 45^\circ = 315^\circ \).
Follow the \( 315^\circ \) arrow.
Step 5: Next, \( -\frac{11\pi}{6} \)
Convert to degrees:
\( -\frac{11\pi}{6} \times \frac{180^\circ}{\pi} = -11 \times 30^\circ = -330^\circ \).
Follow the \( -330^\circ \) arrow.
Step 6: Next, \( 340^\circ \) (Wait, no—wait, after \( -330^\circ \), we follow the arrow to \( 340^\circ \)? Wait, no, let’s check again. Wait, maybe I made a mistake. Let’s re-examine the maze.
Wait, after \( \frac{7\pi}{4} \) (315°), the arrow leads to \( -\frac{11\pi}{6} \). Converting \( -\frac{11\pi}{6} \): \( -\frac{11\pi}{6} \times \frac{180^\circ}{\pi} = -330^\circ \). Then follow the \( -330^\circ \) arrow to \( 340^\circ \)? No, wait, the \( 340^\circ \) arrow is connected. Wait, maybe I skipped a step. Let’s correct:
After \( 420^\circ \) (from \( \frac{7\pi}{3} \)), we go to \( \frac{7\pi}{4} \) (315°). Then from \( \frac{7\pi}{4} \), the arrow is \( 315^\circ \), leading to \( -\frac{11\pi}{6} \). Convert \( -\frac{11\pi}{6} \): \( -330^\circ \). Then follow \( -330^\circ \) to \( 340^\circ \)? Wait, no, the \( 340^\circ \) arrow is next. Then from \( 340^\circ \), follow the arrow to \( -535^\circ \)? Wait, no, let’s check the bottom row.
Wait, maybe a better approach: Let’s list all conversions and follow the correct path.
- Start: \( \frac{\pi}{18}
ightarrow 10^\circ \) (correct, \( \frac{\pi}{18} \times \frac{180}{\pi} = 10^\circ \)).
- \( 10^\circ \) leads to \( -\frac{3\pi}{2} \). Convert \( -\frac{3\pi}{2} \): \( -\frac{3\pi}{2} \times \frac{180}{\pi} = -270^\circ \). So follow \( -270^\circ \) arrow.
- \( -270^\circ \) leads to \( \frac{7\pi}{3} \). Convert \( \frac{7\pi}{3} \): \( \frac{7\pi}{3} \times \frac{180}{\pi} = 420^\circ \). Follow \( 420^\circ \) arrow.
- \( 420^\circ \) leads to \( \frac{7\pi}{4} \). Convert \( \frac{7\pi}{4} \): \( \frac{7\pi}{4} \times \frac{180}{\pi} = 315^\circ \). Follow \( 315^\circ \) arrow.
- \( 315^\circ \) leads to \( -\frac{11\pi}{6} \). Convert \( -\frac{11\pi}{6} \): \( -\frac{11\pi}{6} \times \frac{180}{\pi} = -330^\circ \). Follow \( -330^\circ \) arrow.
- \( -330^\circ \) leads to \( 340^\circ \). Now, \( 340^\circ \) is a degree, but we need to follow the arrow. Wait, \( 340^\circ \) leads to \( -535^\circ \)? Wait, no, the bottom row has \( -535^\circ \) leading to “Finish!”. Wait, let’s check \( 340^\circ \)’s arrow. From \( 340^\circ \), the arrow goes to \( -535^\circ \)? Wait, the bottom right has “Finish!” next to \( -535^\circ \). Wait, let’s convert \( -535^\circ \)? No, \( -535^\circ \) is a degree, but maybe the last step is \( -535^\circ \) leading to Finish.
Wait, maybe I made a mistake in the path. Let’s confirm each conversion:
- \( \frac{\pi}{18} \): \( 10^\circ \) (correct).
-…
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To solve the maze, we convert radians to degrees using the formula \( \text{Degrees} = \text{Radians} \times \frac{180^\circ}{\pi} \). Let's go step by step:
Step 1: Start with \( \frac{\pi}{18} \)
Using the conversion formula:
\( \frac{\pi}{18} \times \frac{180^\circ}{\pi} = \frac{180^\circ}{18} = 10^\circ \).
So we follow the \( 10^\circ \) arrow.
Step 2: Next, \( -\frac{3\pi}{2} \)
Convert to degrees:
\( -\frac{3\pi}{2} \times \frac{180^\circ}{\pi} = -3 \times 90^\circ = -270^\circ \).
Follow the \( -270^\circ \) arrow.
Step 3: Next, \( \frac{7\pi}{3} \)
Convert to degrees:
\( \frac{7\pi}{3} \times \frac{180^\circ}{\pi} = 7 \times 60^\circ = 420^\circ \).
Follow the \( 420^\circ \) arrow.
Step 4: Next, \( \frac{7\pi}{4} \)
Convert to degrees:
\( \frac{7\pi}{4} \times \frac{180^\circ}{\pi} = 7 \times 45^\circ = 315^\circ \).
Follow the \( 315^\circ \) arrow.
Step 5: Next, \( -\frac{11\pi}{6} \)
Convert to degrees:
\( -\frac{11\pi}{6} \times \frac{180^\circ}{\pi} = -11 \times 30^\circ = -330^\circ \).
Follow the \( -330^\circ \) arrow.
Step 6: Next, \( 340^\circ \) (Wait, no—wait, after \( -330^\circ \), we follow the arrow to \( 340^\circ \)? Wait, no, let’s check again. Wait, maybe I made a mistake. Let’s re-examine the maze.
Wait, after \( \frac{7\pi}{4} \) (315°), the arrow leads to \( -\frac{11\pi}{6} \). Converting \( -\frac{11\pi}{6} \): \( -\frac{11\pi}{6} \times \frac{180^\circ}{\pi} = -330^\circ \). Then follow the \( -330^\circ \) arrow to \( 340^\circ \)? No, wait, the \( 340^\circ \) arrow is connected. Wait, maybe I skipped a step. Let’s correct:
After \( 420^\circ \) (from \( \frac{7\pi}{3} \)), we go to \( \frac{7\pi}{4} \) (315°). Then from \( \frac{7\pi}{4} \), the arrow is \( 315^\circ \), leading to \( -\frac{11\pi}{6} \). Convert \( -\frac{11\pi}{6} \): \( -330^\circ \). Then follow \( -330^\circ \) to \( 340^\circ \)? Wait, no, the \( 340^\circ \) arrow is next. Then from \( 340^\circ \), follow the arrow to \( -535^\circ \)? Wait, no, let’s check the bottom row.
Wait, maybe a better approach: Let’s list all conversions and follow the correct path.
- Start: \( \frac{\pi}{18}
ightarrow 10^\circ \) (correct, \( \frac{\pi}{18} \times \frac{180}{\pi} = 10^\circ \)).
- \( 10^\circ \) leads to \( -\frac{3\pi}{2} \). Convert \( -\frac{3\pi}{2} \): \( -\frac{3\pi}{2} \times \frac{180}{\pi} = -270^\circ \). So follow \( -270^\circ \) arrow.
- \( -270^\circ \) leads to \( \frac{7\pi}{3} \). Convert \( \frac{7\pi}{3} \): \( \frac{7\pi}{3} \times \frac{180}{\pi} = 420^\circ \). Follow \( 420^\circ \) arrow.
- \( 420^\circ \) leads to \( \frac{7\pi}{4} \). Convert \( \frac{7\pi}{4} \): \( \frac{7\pi}{4} \times \frac{180}{\pi} = 315^\circ \). Follow \( 315^\circ \) arrow.
- \( 315^\circ \) leads to \( -\frac{11\pi}{6} \). Convert \( -\frac{11\pi}{6} \): \( -\frac{11\pi}{6} \times \frac{180}{\pi} = -330^\circ \). Follow \( -330^\circ \) arrow.
- \( -330^\circ \) leads to \( 340^\circ \). Now, \( 340^\circ \) is a degree, but we need to follow the arrow. Wait, \( 340^\circ \) leads to \( -535^\circ \)? Wait, no, the bottom row has \( -535^\circ \) leading to “Finish!”. Wait, let’s check \( 340^\circ \)’s arrow. From \( 340^\circ \), the arrow goes to \( -535^\circ \)? Wait, the bottom right has “Finish!” next to \( -535^\circ \). Wait, let’s convert \( -535^\circ \)? No, \( -535^\circ \) is a degree, but maybe the last step is \( -535^\circ \) leading to Finish.
Wait, maybe I made a mistake in the path. Let’s confirm each conversion:
- \( \frac{\pi}{18} \): \( 10^\circ \) (correct).
- \( -\frac{3\pi}{2} \): \( -270^\circ \) (correct, \( -\frac{3\pi}{2} \times \frac{180}{\pi} = -270^\circ \)).
- \( \frac{7\pi}{3} \): \( 420^\circ \) (correct, \( \frac{7\pi}{3} \times \frac{180}{\pi} = 420^\circ \)).
- \( \frac{7\pi}{4} \): \( 315^\circ \) (correct, \( \frac{7\pi}{4} \times \frac{180}{\pi} = 315^\circ \)).
- \( -\frac{11\pi}{6} \): \( -330^\circ \) (correct, \( -\frac{11\pi}{6} \times \frac{180}{\pi} = -330^\circ \)).
- \( 340^\circ \): Now, \( 340^\circ \) is a degree, but we need to follow the arrow to the next radian or degree. Wait, the \( 340^\circ \) arrow leads to \( -535^\circ \)? Wait, the bottom row has \( -535^\circ \) next to “Finish!”. Let’s check \( -535^\circ \): Is there a radian that converts to \( -535^\circ \)? Let’s see: \( -535^\circ \times \frac{\pi}{180^\circ} = -\frac{107\pi}{36} \) (since \( 535 \div 5 = 107 \), \( 36 \times 5 = 180 \)? Wait, \( 535 \times \frac{\pi}{180} = \frac{107\pi}{36} \) (since \( 535 = 107 \times 5 \), \( 180 = 36 \times 5 \), so \( \frac{535\pi}{180} = \frac{107\pi}{36} \), so \( -535^\circ = -\frac{107\pi}{36} \)? Wait, no: \( -535^\circ \times \frac{\pi}{180} = -\frac{107\pi}{36} \) (because \( 535 \div 5 = 107 \), \( 180 \div 5 = 36 \)). So \( -\frac{107\pi}{36} \) converts to \( -535^\circ \) (since \( -\frac{107\pi}{36} \times \frac{180}{\pi} = -107 \times 5 = -535^\circ \)).
So the path is:
\( \frac{\pi}{18}
ightarrow 10^\circ
ightarrow -\frac{3\pi}{2}
ightarrow -270^\circ
ightarrow \frac{7\pi}{3}
ightarrow 420^\circ
ightarrow \frac{7\pi}{4}
ightarrow 315^\circ
ightarrow -\frac{11\pi}{6}
ightarrow -330^\circ
ightarrow 340^\circ
ightarrow -535^\circ
ightarrow \) Finish!
Final Path Summary:
- \( \frac{\pi}{18} \) (Start) → \( 10^\circ \)
- \( 10^\circ \) → \( -\frac{3\pi}{2} \)
- \( -\frac{3\pi}{2} \) → \( -270^\circ \)
- \( -270^\circ \) → \( \frac{7\pi}{3} \)
- \( \frac{7\pi}{3} \) → \( 420^\circ \)
- \( 420^\circ \) → \( \frac{7\pi}{4} \)
- \( \frac{7\pi}{4} \) → \( 315^\circ \)
- \( 315^\circ \) → \( -\frac{11\pi}{6} \)
- \( -\frac{11\pi}{6} \) → \( -330^\circ \)
- \( -330^\circ \) → \( 340^\circ \)
- \( 340^\circ \) → \( -535^\circ \) (leads to Finish)
To confirm, each conversion is correct using \( \text{Degrees} = \text{Radians} \times \frac{180^\circ}{\pi} \). The key is to follow the arrows with matching conversions.