To evaluate tan(7\u03c0\/6)<\/strong> using the unit circle:<\/p>\n\n\n\n tan\u2061(7\u03c06)=13\\tan\\left(\\frac{7\\pi}{6}\\right) = \\frac{1}{\\sqrt{3}}tan(67\u03c0\u200b)=3\u200b1\u200b<\/p>\n\n\n\n But because 7\u03c0\/6 is in the third quadrant, where tangent is positive<\/strong>, and both sine and cosine are negative<\/strong>, the tangent value is:tan\u2061(7\u03c06)=\u221212\u221232=13=33\\tan\\left(\\frac{7\\pi}{6}\\right) = \\frac{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}} = \\frac{1}{\\sqrt{3}} = \\frac{\\sqrt{3}}{3}tan(67\u03c0\u200b)=\u221223\u200b\u200b\u221221\u200b\u200b=3\u200b1\u200b=33\u200b\u200b<\/p>\n\n\n\n To evaluate tan(7\u03c0\/6)<\/strong>, begin by understanding what this angle represents on the unit circle<\/strong>. The unit circle is a circle of radius 1 centered at the origin in the coordinate plane. Each angle on the unit circle corresponds to a point whose coordinates are given by (cos \u03b8, sin \u03b8)<\/strong>. The tangent of an angle is defined as:tan\u2061(\u03b8)=sin\u2061(\u03b8)cos\u2061(\u03b8)\\tan(\\theta) = \\frac{\\sin(\\theta)}{\\cos(\\theta)}tan(\u03b8)=cos(\u03b8)sin(\u03b8)\u200b<\/p>\n\n\n\n Now, consider 7\u03c0\/6<\/strong>. This angle is slightly more than \u03c0 (which is 6\u03c0\/6). So:7\u03c06=\u03c0+\u03c06\\frac{7\\pi}{6} = \\pi + \\frac{\\pi}{6}67\u03c0\u200b=\u03c0+6\u03c0\u200b<\/p>\n\n\n\n This tells us that 7\u03c0\/6<\/strong> is located in the third quadrant<\/strong> of the unit circle. In this quadrant, sine<\/strong> and cosine<\/strong> values are both negative<\/strong>, and since tangent is sine divided by cosine, tangent becomes positive<\/strong> in this quadrant.<\/p>\n\n\n\n To find the exact values of sine and cosine, use the reference angle<\/strong>. The reference angle for 7\u03c0\/6 is:7\u03c06\u2212\u03c0=\u03c06\\frac{7\\pi}{6} – \\pi = \\frac{\\pi}{6}67\u03c0\u200b\u2212\u03c0=6\u03c0\u200b<\/p>\n\n\n\n From known values on the unit circle:<\/p>\n\n\n\n So for 7\u03c0\/6, since it’s in the third quadrant:<\/p>\n\n\n\n Now compute tangent:tan\u2061(7\u03c06)=\u221212\u221232=13=33\\tan\\left(\\frac{7\\pi}{6}\\right) = \\frac{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}} = \\frac{1}{\\sqrt{3}} = \\frac{\\sqrt{3}}{3}tan(67\u03c0\u200b)=\u221223\u200b\u200b\u221221\u200b\u200b=3\u200b1\u200b=33\u200b\u200b<\/p>\n\n\n\n Therefore, the final answer is \u221a3\u20443<\/strong>.<\/p>\n\n\n\n Use the unit circle to evaluate the function. tan 7pi\/6 The Correct Answer and Explanation is: To evaluate tan(7\u03c0\/6) using the unit circle: Correct Answer: tan\u2061(7\u03c06)=13\\tan\\left(\\frac{7\\pi}{6}\\right) = \\frac{1}{\\sqrt{3}}tan(67\u03c0\u200b)=3\u200b1\u200b But because 7\u03c0\/6 is in the third quadrant, where tangent is positive, and both sine and cosine are negative, the tangent value is:tan\u2061(7\u03c06)=\u221212\u221232=13=33\\tan\\left(\\frac{7\\pi}{6}\\right) = \\frac{-\\frac{1}{2}}{-\\frac{\\sqrt{3}}{2}} = \\frac{1}{\\sqrt{3}} […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-30894","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/30894","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=30894"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/30894\/revisions"}],"predecessor-version":[{"id":30899,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/30894\/revisions\/30899"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=30894"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=30894"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=30894"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Correct Answer:<\/strong><\/h3>\n\n\n\n
\n\n\n\nDetailed Explanation<\/strong><\/h3>\n\n\n\n
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