{"status": "success", "data": {"description_md": "For how many values of $x$ in $[0,\\pi]$ is $\\sin^{ - 1}(\\sin 6x) = \\cos^{ - 1}(\\cos x)$?<br>Note: The functions $\\sin^{ - 1} = \\arcsin$ and $\\cos^{ - 1} = \\arccos$ denote inverse trigonometric functions.\n\n$\\textbf{(A)}\\ 3\\qquad \\textbf{(B)}\\ 4\\qquad \\textbf{(C)}\\ 5\\qquad \\textbf{(D)}\\ 6\\qquad \\textbf{(E)}\\ 7$\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>For how many values of <span class=\"katex--inline\">x</span> in <span class=\"katex--inline\">[0,\\pi]</span> is <span class=\"katex--inline\">\\sin^{ - 1}(\\sin 6x) = \\cos^{ - 1}(\\cos x)</span>?<br/>Note: The functions <span class=\"katex--inline\">\\sin^{ - 1} = \\arcsin</span> and <span class=\"katex--inline\">\\cos^{ - 1} = \\arccos</span> denote inverse trigonometric functions.</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}\\ 3\\qquad \\textbf{(B)}\\ 4\\qquad \\textbf{(C)}\\ 5\\qquad \\textbf{(D)}\\ 6\\qquad \\textbf{(E)}\\ 7</span></p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2009 AMC 12B Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc12B_p25", "prev": "/problem/09_amc12B_p23"}}