{"id":34528,"date":"2025-06-23T16:20:47","date_gmt":"2025-06-23T16:20:47","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=34528"},"modified":"2025-06-23T16:20:49","modified_gmt":"2025-06-23T16:20:49","slug":"value-of-sin-135-in-simplest-form-with-a-rational-find-the-exact-denominator","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/value-of-sin-135-in-simplest-form-with-a-rational-find-the-exact-denominator\/","title":{"rendered":"value of sin 135′ in simplest form with a rational Find the exact denominator"},"content":{"rendered":"\n

value of sin 135′ in simplest form with a rational Find the exact denominator:<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The exact value of sin 135\u00b0<\/strong> in simplest form with a rational denominator is:sin\u2061135\u2218=22\\sin 135^\\circ = \\frac{\\sqrt{2}}{2}sin135\u2218=22\u200b\u200b<\/p>\n\n\n\n

\n\n\n\n

Explanation:<\/h3>\n\n\n\n

To find the exact value of sin 135\u00b0<\/strong>, we can use our knowledge of reference angles and the unit circle.<\/p>\n\n\n\n

First, note that 135\u00b0 lies in the second quadrant<\/strong>. Angles in the second quadrant range from 90\u00b0 to 180\u00b0, and for these angles, the sine function is positive<\/strong>. This is important because the sign of the trigonometric function depends on the quadrant in which the angle lies.<\/p>\n\n\n\n

To simplify sin 135\u00b0, we find its reference angle<\/strong>. The reference angle is the acute angle formed between the terminal side of the given angle and the x-axis. For 135\u00b0, the reference angle is:180\u2218\u2212135\u2218=45\u2218180^\\circ – 135^\\circ = 45^\\circ180\u2218\u2212135\u2218=45\u2218<\/p>\n\n\n\n

So, sin 135\u00b0 has the same absolute value as sin 45\u00b0, but since it lies in the second quadrant and sine is positive there, we have:sin\u2061135\u2218=sin\u206145\u2218\\sin 135^\\circ = \\sin 45^\\circsin135\u2218=sin45\u2218<\/p>\n\n\n\n

Now we need to recall the exact value of sin 45\u00b0. This is a common angle in trigonometry, and its sine is:sin\u206145\u2218=22\\sin 45^\\circ = \\frac{\\sqrt{2}}{2}sin45\u2218=22\u200b\u200b<\/p>\n\n\n\n

Therefore:sin\u2061135\u2218=22\\sin 135^\\circ = \\frac{\\sqrt{2}}{2}sin135\u2218=22\u200b\u200b<\/p>\n\n\n\n

This value is already in its simplest form and has a rationalized denominator<\/strong>. A rational denominator means that the denominator is a rational number. In this case, 2 is a rational number, and the irrational part (\u221a2) is in the numerator. Thus, the answer is both exact and properly simplified.<\/p>\n\n\n\n

This value is used often in trigonometry, geometry, and physics. It is one of the standard values students are encouraged to memorize because it helps solve a wide variety of problems involving angles, especially those related to 45\u00b0, 135\u00b0, and their equivalents in radians.<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

value of sin 135′ in simplest form with a rational Find the exact denominator: The Correct Answer and Explanation is: The exact value of sin 135\u00b0 in simplest form with a rational denominator is:sin\u2061135\u2218=22\\sin 135^\\circ = \\frac{\\sqrt{2}}{2}sin135\u2218=22\u200b\u200b Explanation: To find the exact value of sin 135\u00b0, we can use our knowledge of reference angles and […]<\/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-34528","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34528","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=34528"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34528\/revisions"}],"predecessor-version":[{"id":34537,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34528\/revisions\/34537"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=34528"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=34528"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=34528"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}