{"id":42706,"date":"2025-06-29T08:54:18","date_gmt":"2025-06-29T08:54:18","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=42706"},"modified":"2025-06-29T08:54:19","modified_gmt":"2025-06-29T08:54:19","slug":"find-the-exact-value-of-each-trigonometric-function-sin-300","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/find-the-exact-value-of-each-trigonometric-function-sin-300\/","title":{"rendered":"Find the exact value of each trigonometric function sin 300"},"content":{"rendered":"\n<p>Find the exact value of each trigonometric function sin 300<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the exact value of sin\u2061(300\u2218)\\sin(300^\\circ)sin(300\u2218), we need to first understand where 300\u2218300^\\circ300\u2218 lies on the unit circle.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Determine the reference angle<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The angle 300\u2218300^\\circ300\u2218 is in the fourth quadrant of the unit circle.<\/li>\n\n\n\n<li>To find the reference angle, subtract 300\u2218300^\\circ300\u2218 from 360\u2218360^\\circ360\u2218: 360\u2218\u2212300\u2218=60\u2218360^\\circ &#8211; 300^\\circ = 60^\\circ360\u2218\u2212300\u2218=60\u2218<\/li>\n<\/ul>\n\n\n\n<p>Thus, the reference angle for 300\u2218300^\\circ300\u2218 is 60\u221860^\\circ60\u2218.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Determine the sign in the fourth quadrant<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In the fourth quadrant, the sine function is negative because the yyy-coordinate of points on the unit circle is negative in this quadrant.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Use the known value of sine for the reference angle<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>We know that sin\u2061(60\u2218)=32\\sin(60^\\circ) = \\frac{\\sqrt{3}}{2}sin(60\u2218)=23\u200b\u200b.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Apply the sign<\/h3>\n\n\n\n<p>Since 300\u2218300^\\circ300\u2218 is in the fourth quadrant, and sine is negative in the fourth quadrant, the value of sin\u2061(300\u2218)\\sin(300^\\circ)sin(300\u2218) is: sin\u2061(300\u2218)=\u2212sin\u2061(60\u2218)=\u221232\\sin(300^\\circ) = -\\sin(60^\\circ) = -\\frac{\\sqrt{3}}{2}sin(300\u2218)=\u2212sin(60\u2218)=\u221223\u200b\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>The exact value of sin\u2061(300\u2218)\\sin(300^\\circ)sin(300\u2218) is \u221232-\\frac{\\sqrt{3}}{2}\u221223\u200b\u200b.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-362.jpeg\" alt=\"\" class=\"wp-image-42707\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-362.jpeg 1024w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-362-300x300.jpeg 300w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-362-150x150.jpeg 150w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-362-768x768.jpeg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Find the exact value of each trigonometric function sin 300 The Correct Answer and Explanation is: To find the exact value of sin\u2061(300\u2218)\\sin(300^\\circ)sin(300\u2218), we need to first understand where 300\u2218300^\\circ300\u2218 lies on the unit circle. Step 1: Determine the reference angle Thus, the reference angle for 300\u2218300^\\circ300\u2218 is 60\u221860^\\circ60\u2218. Step 2: Determine the sign in [&hellip;]<\/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-42706","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42706","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=42706"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42706\/revisions"}],"predecessor-version":[{"id":42708,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42706\/revisions\/42708"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=42706"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=42706"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=42706"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}