{"id":18505,"date":"2022-07-29T09:57:17","date_gmt":"2022-07-29T04:27:17","guid":{"rendered":"https:\/\/apboardsolutions.com\/?p=18505"},"modified":"2023-03-30T15:04:19","modified_gmt":"2023-03-30T09:34:19","slug":"inter-1st-year-maths-1a-trigonometric-equations-formulas","status":"publish","type":"post","link":"https:\/\/apboardsolutions.com\/inter-1st-year-maths-1a-trigonometric-equations-formulas\/","title":{"rendered":"Inter 1st Year Maths 1A Trigonometric Equations Formulas"},"content":{"rendered":"

Use these Inter 1st Year Maths 1A Formulas<\/a> PDF Chapter 7 Trigonometric Equations Functions to solve questions creatively.<\/p>\n

Intermediate 1st Year Maths 1A Trigonometric Equations Formulas<\/h2>\n

\u2192 If K \u2208 [-1, 1], then the principal solution \u03b8 of sin \u03b8 = K lies in \\(\\left[\\frac{-\\pi}{2}, \\frac{\\pi}{2}\\right]\\)and the general solution is given by n\u03c0 + (-1)n<\/sup> \u03b8, n \u2208 Z<\/p>\n

\u2192 If K \u2208 [-1, 1], then the principal solution \u03b8 of cos \u03b8 = K lies in [0, \u03c0] and the general solution is given by 2n\u03c0 \u00b1 0, n \u2208 Z<\/p>\n

\u2192 If K \u2208 R, then the principal solution \u03b8 of tan x = K lies in \\(\\left(\\frac{-\\pi}{2}, \\frac{\\pi}{2}\\right)\\), and the general solution is given by n\\left(\\frac{-\\pi}{2}, \\frac{\\pi}{2}\\right) \u00b1 \u03b8, n \u2208 Z<\/p>\n

\u2192 sin \u03b8 = 0 \u21d2 \u03b8 = n\u03c0, n is an integer and its principal solution is x = 0<\/p>\n

\u2192 cos \u03b8 = 0 \u21d2 \u03b8 = (2n + 1)\\(\\frac{\\pi}{2}\\), n is an integer and its principal solution is x = \\(\\frac{\\pi}{2}\\)<\/p>\n

\u2192 tan \u03b8 = 0 \u21d2 \u03b8 = n\u03c0, n is an integer and its principal solution is x = 0<\/p>\n

\u2192 cot \u03b8 = 0 \u21d2 \u03b8 = (2n + 1)\\(\\frac{\\pi}{2}\\) n is an integer<\/p>\n

\u2192 cosec \u03b8 = cosec \u03b1 \u21d2 \u03b8 = n\u03c0 + (-1)n<\/sup>\u03b1, n is an integer<\/p>\n

\u2192 sec \u03b8 = sec \u03b1 \u21d2 \u03b8 = 2n\u03c0 \u00b1 \u03b1, n is an integer<\/p>\n

\"Inter<\/p>\n

\u2192 cot \u03b8 = cot \u03b1 \u21d2 \u03b8 = n\u03c0 \u00b1 \u03b1 and the principal solution \u03b1 \u2208 (0, \u03c0)<\/p>\n

\u2192 sin2<\/sup>\u03b8 = sin2<\/sup> \u03b1 \u21d2 \u03b8 = n\u03c0 \u00b1 \u03b1, wherenever a solution exists.<\/p>\n

\u2192 cos2<\/sup>\u03b8 = cos2<\/sup> \u03b1 \u21d2 \u03b8 = n\u03c0 \u00b1 \u03b1, wherenever a solution exists.<\/p>\n

\u2192 tan2<\/sup>\u03b8 = tan2<\/sup> \u03b1 \u21d2 \u03b8 = n\u03c0 \u00b1 \u03b1, wherenever a solution exists.<\/p>\n

\u2192 a cos \u03b8 + b sin \u03b8 = c, (a, b, c) \u2208 R and a2<\/sup> + b2<\/sup> \u2260 0 has a solution, iff c2<\/sup> \u2264 a2<\/sup> + b2<\/sup>.<\/p>\n

Trigonometric Equations:
\nAn equation consisting of the trigonometric functions of a variable angle \u03b8 \u2208 R is called a trigonometric equation.<\/p>\n

\u2192 sin \u03b8 = 0 \u21d2 \u03b8 = n\u03c0, where n \u2208 Z.<\/p>\n

\u2192 cos \u03b8 = 0 \u21d2 \u03b8 = (2n + 1)\\(\\), where n \u2208 Z.<\/p>\n

\u2192 tan \u03b8 = 0 \u21d2 \u03b8 = n\u03c0 where \u03c0 is any integer.<\/p>\n

\u2192 The solution of sin \u03b8 = k (|k|<1) lying between – \\(\\frac{\\pi}{2}\\) and \\(\\frac{\\pi}{2}\\) is called the principle solution of the equation.<\/p>\n

\u2192 The solution of cos \u03b8 = k (|k|<1) lying between 0 and \u03c0 is called the principal solution of the equation.<\/p>\n

\u2192 That solution of tan \u03b8 = k, lying between – \\(\\frac{\\pi}{2}\\) and \\(\\frac{\\pi}{2}\\) is called the principal solution of the equation.<\/p>\n

\u2192 The general value of \u03b8 satisfying cos \u03b8 = k (|k| < 1) is given by \u03b8 = 2n\u03c0 \u00b1 \u03b1 where n \u2208Z.<\/p>\n

\u2192 The general value of \u03b8 satisfying sin \u03b8 = k (|k|< 1) is given by \u03b8 = n\u03c0 + (-1)n<\/sup>\u03b1 where n \u2208 Z.<\/p>\n

\u2192 The general value of \u03b8 satisfying tan \u03b8 = k is given by \u03b8 = n\u03c0 + \u03b1 where n \u2208 Z. (in each of the above cases, \u03b1 is the principal solution).<\/p>\n

\u2192 If sin0 = k, tan0 = k are given equations, then the general value of \u03b8 is given by \u03b8 = 2n\u03c0 + \u03b1 where \u03b1 is that solution lying between 0 and 2\u03c0.<\/p>\n

\u2192 The equation a cos \u03b8 + b sin \u03b8 = c will have no solution or will be inconsistent if |c| > \\(\\sqrt{a^{2}+b^{2}}\\)<\/p>\n

\u2192 cos n\u03c0 = (-1)n<\/sup> , sin n\u03c0 = 0.<\/p>\n

\u2192 If sin2<\/sup>\u03b8 = sin2<\/sup>\u03b1 or cos2<\/sup>\u03b8 = cos2<\/sup>\u03b1 or tan2<\/sup>\u03b8 = tan2<\/sup>a, then \u03b8 = n\u03c0 \u00b1 \u03b1; n \u2208 Z.<\/p>\n","protected":false},"excerpt":{"rendered":"

Use these Inter 1st Year Maths 1A Formulas PDF Chapter 7 Trigonometric Equations Functions to solve questions creatively. Intermediate 1st Year Maths 1A Trigonometric Equations Formulas \u2192 If K \u2208 [-1, 1], then the principal solution \u03b8 of sin \u03b8 = K lies in and the general solution is given by n\u03c0 + (-1)n \u03b8, … Read more<\/a><\/p>\n","protected":false},"author":4,"featured_media":39264,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[13],"tags":[],"jetpack_featured_media_url":"https:\/\/apboardsolutions.com\/wp-content\/uploads\/2022\/07\/Trigonometric-Equations-Formulas.png","_links":{"self":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts\/18505"}],"collection":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/comments?post=18505"}],"version-history":[{"count":3,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts\/18505\/revisions"}],"predecessor-version":[{"id":20003,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts\/18505\/revisions\/20003"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/media\/39264"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/media?parent=18505"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/categories?post=18505"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/tags?post=18505"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}