pre - calculus honors 2024\n9.5 hmwk:polar coordinates (homework)\ncurrent score\nquestion 1 2 3 4 5 6 7 8 9…
pre - calculus honors 2024\n9.5 hmwk:polar coordinates (homework)\ncurrent score\nquestion 1 2 3 4 5 6 7 8 9 10\npoints 0.8408 0.8408 0.8408 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8\ntotal score 3.02/8 37.8%\nassignment submission & scoring\nassignment submission\nfor this assignment, you submit answers by question parts. the number of submissions remaining for each question\nassignment scoring\nyour last submission is used for your score.\n8. -/0.8 points details my notes larpcalclimag48 9.5.039.mi.\nconvert the rectangular equation to polar form.\nx² + y² = 64\nneed help? read it watch it master it\nshow my work (optional) \nsubmit answer
Answer
Explanation:
Step1: Recall conversion formulas
In polar - rectangular conversion, $x = r\cos\theta$ and $y = r\sin\theta$.
Step2: Substitute into the given equation
Substitute $x = r\cos\theta$ and $y = r\sin\theta$ into $x^{2}+y^{2}=64$. We get $(r\cos\theta)^{2}+(r\sin\theta)^{2}=64$.
Step3: Simplify the equation
Expand the left - hand side: $r^{2}\cos^{2}\theta + r^{2}\sin^{2}\theta=64$. Factor out $r^{2}$: $r^{2}(\cos^{2}\theta+\sin^{2}\theta)=64$. Since $\cos^{2}\theta+\sin^{2}\theta = 1$, the equation simplifies to $r^{2}=64$.
Step4: Solve for $r$
Take the square root of both sides. We have $r = 8$ or $r=-8$. But in polar coordinates, $r\geq0$ usually represents the distance from the origin, so we take $r = 8$.
Answer:
$r = 8$