train/precalculus/1025.json

{
    "problem": "Convert the point $( -5, 0, -8 )$ in rectangular coordinates to cylindrical coordinates.  Enter your answer in the form $(r,\\theta,z),$ where $r > 0$ and $0 \\le \\theta < 2 \\pi.$",
    "level": "Level 3",
    "type": "Precalculus",
    "solution": "We have that $r = \\sqrt{(-5)^2 + 0^2} = 5.$  We want $\\theta$ to satisfy\n\\begin{align*}\n-5 &= 5 \\cos \\theta, \\\\\n0 &= 5 \\sin \\theta.\n\\end{align*}Thus, $\\theta = \\pi,$ so the cylindrical coordinates are $\\boxed{(5,\\pi,-8)}.$"
}