{"status": "success", "data": {"description_md": "How many values of $\\theta$ in the interval $0<\\theta\\le 2\\pi$ satisfy$$1-3\\sin\\theta+5\\cos3\\theta = 0?$$\n\n$\\textbf{(A) }2 \\qquad \\textbf{(B) }4 \\qquad \\textbf{(C) }5\\qquad \\textbf{(D) }6 \\qquad \\textbf{(E) }8$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>How many values of  <span class=\"katex--inline\">\\theta</span>  in the interval  <span class=\"katex--inline\">0&lt;\\theta\\le 2\\pi</span>  satisfy <span class=\"katex--display\">1-3\\sin\\theta+5\\cos3\\theta = 0?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }2 \\qquad \\textbf{(B) }4 \\qquad \\textbf{(C) }5\\qquad \\textbf{(D) }6 \\qquad \\textbf{(E) }8</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2021 AMC 12B Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/21_amc12B_p14", "prev": "/problem/21_amc12B_p12"}}