Evaluate the following and indicate the reference angle 1. Tan 330 degrees<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n Evaluate:<\/strong> tan\u2061330\u2218\\tan 330^\\circ The reference angle is the acute angle formed between the given angle and the nearest x-axis. Since 330\u2218330^\\circ is in the fourth quadrant (because it is between 270\u2218270^\\circ and 360\u2218360^\\circ), the reference angle is calculated by subtracting 330\u2218330^\\circ from 360\u2218360^\\circ: Reference angle=360\u2218\u2212330\u2218=30\u2218\\text{Reference angle} = 360^\\circ – 330^\\circ = 30^\\circ<\/p>\n\n\n\n The tangent function in the fourth quadrant is negative because tangent is positive in the first and third quadrants and negative in the second and fourth quadrants.<\/p>\n\n\n\n We use the reference angle of 30\u221830^\\circ to find the tangent value: tan\u206130\u2218=13=33\\tan 30^\\circ = \\frac{1}{\\sqrt{3}} = \\frac{\\sqrt{3}}{3}<\/p>\n\n\n\n Since 330\u2218330^\\circ is in the fourth quadrant, tan\u2061330\u2218\\tan 330^\\circ will be negative: tan\u2061330\u2218=\u2212tan\u206130\u2218=\u221233\\tan 330^\\circ = -\\tan 30^\\circ = -\\frac{\\sqrt{3}}{3}<\/p>\n\n\n\n tan\u2061330\u2218=\u221233\\tan 330^\\circ = -\\frac{\\sqrt{3}}{3} Reference angle=30\u2218\\text{Reference angle} = 30^\\circ<\/p>\n\n\n\n The tangent function is defined as the ratio of the sine to the cosine of the angle. Angles on the unit circle repeat every 360\u2218360^\\circ, so angles greater than 360\u2218360^\\circ or negative angles can be converted to equivalent angles between 0\u22180^\\circ and 360\u2218360^\\circ.<\/p>\n\n\n\n The angle 330\u2218330^\\circ lies in the fourth quadrant, where cosine is positive and sine is negative. Because tangent is sine divided by cosine, tangent in the fourth quadrant is negative.<\/p>\n\n\n\n To evaluate the tangent at 330\u2218330^\\circ, the angle is related to the acute reference angle of 30\u221830^\\circ. Reference angles simplify trigonometric calculations by allowing the use of well-known values for acute angles.<\/p>\n\n\n\n Knowing tan\u206130\u2218=13\\tan 30^\\circ = \\frac{1}{\\sqrt{3}}, the sign of tangent at 330\u2218330^\\circ is determined by the quadrant. Since the fourth quadrant tangent is negative, the answer becomes \u221213-\\frac{1}{\\sqrt{3}}, often rationalized to \u221233-\\frac{\\sqrt{3}}{3}.<\/p>\n\n\n\n The reference angle is essential for understanding the relationship between the given angle and its trigonometric function value without needing a calculator or a unit circle chart for every angle.<\/p>\n","protected":false},"excerpt":{"rendered":" Evaluate the following and indicate the reference angle 1. Tan 330 degrees The correct answer and explanation is: Evaluate: tan\u2061330\u2218\\tan 330^\\circReference Angle: ? Step 1: Find the reference angle The reference angle is the acute angle formed between the given angle and the nearest x-axis. Since 330\u2218330^\\circ is in the fourth quadrant (because it is […]<\/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-38289","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38289","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=38289"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38289\/revisions"}],"predecessor-version":[{"id":38290,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38289\/revisions\/38290"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=38289"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=38289"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=38289"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Reference Angle:<\/strong> ?<\/p>\n\n\n\n
\n\n\n\nStep 1: Find the reference angle<\/h3>\n\n\n\n
\n\n\n\nStep 2: Find tan\u2061330\u2218\\tan 330^\\circ<\/h3>\n\n\n\n
\n\n\n\nFinal answers:<\/h3>\n\n\n\n
\n\n\n\nExplanation<\/h3>\n\n\n\n