{"id":44476,"date":"2025-06-30T16:16:10","date_gmt":"2025-06-30T16:16:10","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=44476"},"modified":"2025-06-30T16:16:11","modified_gmt":"2025-06-30T16:16:11","slug":"which-of-the-following-statement-is-true-2","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/which-of-the-following-statement-is-true-2\/","title":{"rendered":"‘Which of the following statement is true"},"content":{"rendered":"\n

‘Which of the following statement is true? A. The domain of cosine function is the set of real numbers. B. The domain of the tangent function is the set of all real numbers_ C The range of sine function is the set of all real numbers_ D. The range of cosine function is the set of all real numbers<\/p>\n\n\n\n

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

The correct statement is A<\/strong>: The domain of the cosine function is the set of real numbers.<\/p>\n\n\n\n

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

Let’s break down each option and evaluate it based on the properties of the trigonometric functions involved.<\/p>\n\n\n\n

Option A: The domain of cosine function is the set of real numbers.<\/h4>\n\n\n\n

This statement is true<\/strong>. The cosine function is defined for all real numbers. For any real number input, cosine provides a corresponding output between -1 and 1. Specifically, for any angle \u03b8\\theta\u03b8, cos\u2061(\u03b8)\\cos(\\theta)cos(\u03b8) is a well-defined value. The cosine function is periodic, repeating every 2\u03c02\\pi2\u03c0, but it remains defined for all real values of \u03b8\\theta\u03b8. Hence, the domain of the cosine function is indeed all real numbers, (\u2212\u221e,\u221e)(-\\infty, \\infty)(\u2212\u221e,\u221e).<\/p>\n\n\n\n

Option B: The domain of the tangent function is the set of all real numbers.<\/h4>\n\n\n\n

This statement is false<\/strong>. The domain of the tangent function is not the set of all real numbers because the tangent function has vertical asymptotes at odd multiples of \u03c02\\frac{\\pi}{2}2\u03c0\u200b. This means that tan\u2061(x)\\tan(x)tan(x) is undefined at points where x=\u03c02+n\u03c0x = \\frac{\\pi}{2} + n\\pix=2\u03c0\u200b+n\u03c0 for any integer nnn. Therefore, the domain of the tangent function excludes these points.<\/p>\n\n\n\n

Option C: The range of the sine function is the set of all real numbers.<\/h4>\n\n\n\n

This statement is false<\/strong>. The sine function has a restricted range. The values of sin\u2061(x)\\sin(x)sin(x) are always between -1 and 1, inclusive. So, the range of the sine function is [\u22121,1][-1, 1][\u22121,1], not all real numbers.<\/p>\n\n\n\n

Option D: The range of the cosine function is the set of all real numbers.<\/h4>\n\n\n\n

This statement is also false<\/strong>. Similar to the sine function, the cosine function has a range of values between -1 and 1. The output of cos\u2061(x)\\cos(x)cos(x) is always within the interval [\u22121,1][-1, 1][\u22121,1], not the entire set of real numbers.<\/p>\n\n\n\n

Conclusion:<\/h3>\n\n\n\n

The only correct statement is A<\/strong>, as the cosine function is defined for all real numbers.<\/p>\n\n\n\n

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

‘Which of the following statement is true? A. The domain of cosine function is the set of real numbers. B. The domain of the tangent function is the set of all real numbers_ C The range of sine function is the set of all real numbers_ D. The range of cosine function is the set […]<\/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-44476","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44476","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=44476"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44476\/revisions"}],"predecessor-version":[{"id":44478,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44476\/revisions\/44478"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=44476"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=44476"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=44476"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}