{"id":38429,"date":"2024-02-16T10:01:12","date_gmt":"2024-02-16T04:31:12","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=38429"},"modified":"2024-02-16T17:54:57","modified_gmt":"2024-02-16T12:24:57","slug":"plus-one-maths-notes-chapter-3","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/plus-one-maths-notes-chapter-3\/","title":{"rendered":"Plus One Maths Notes Chapter 3 Trigonometric Functions"},"content":{"rendered":"

Plus One Maths Notes Chapter 3 Trigonometric Functions is part of Plus One Maths Notes<\/a>. Here we have given Kerala Plus One Maths Notes Chapter 3 Trigonometric Functions.<\/p>\n\n\n\n\n\n\n\n\n\n
Board<\/strong><\/td>\nSCERT, Kerala<\/td>\n<\/tr>\n
Text Book<\/strong><\/td>\nNCERT Based<\/td>\n<\/tr>\n
Class<\/strong><\/td>\nPlus One<\/td>\n<\/tr>\n
Subject<\/strong><\/td>\nMaths Notes<\/td>\n<\/tr>\n
Chapter<\/strong><\/td>\nChapter 3<\/td>\n<\/tr>\n
Chapter Name<\/strong><\/td>\nTrigonometric Functions<\/td>\n<\/tr>\n
Category<\/strong><\/td>\nPlus\u00a0One Kerala<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Kerala Plus One Maths Notes Chapter 3 Trigonometric Functions<\/h2>\n

I. Angles<\/span>
\nThe measure of an angle is the amount of rotation performed to get the terminal side from the initial side.<\/p>\n

1. Degree measure: If a rotation from the initial side to terminal side is \\(\\left(\\frac{1}{360}\\right)^{t h}\\) of a revolution, the angle is said to have a measure of one degree, written as 1\u00b0. 1\u00b0 = 60′ and f = 60″.<\/p>\n

2. Radian measure: An angle subtended at the center by an arc of length 1 unit in a unit circle is said to be of 1 radian. Radian measure is a real number corresponding to degree measure.<\/p>\n

180\u00b0 = \u03c0 radians<\/p>\n

Radian measure = \\(\\frac{\\pi}{180}\\) \u00d7 Degree measure<\/p>\n

Degree measure = \\(\\frac{180}{\\pi}\\) \u00d7 Radian measure<\/p>\n

l = r\u03b8, where l = arc length, r = radius of the circle and \u03b8 = angle in radian measure.<\/p>\n

II. Trigonometric Function<\/span>
\nConsider a unit circle with centre at the origin of the coordinate axis.
\nLet P (a, b) be any point on the circle which makes an angle \u03b8\u00b0 with the x-axis. Let x be the corresponding radian measure of the angle \u03b8\u00b0, i.e; x is the arc length corresponding to \u03b8\u00b0.<\/p>\n

\"Plus<\/p>\n

From the \u2206OMP’m the figure we get;
\nsin \u03b8 = sin x = \\(\\frac{b}{1}\\) = b and cos \u03b8 = cos x = \\(\\frac{b}{1}\\) = a
\nThis means that for each real value of x we get corresponding unique \u2018sin\u2019 and \u2018cosine\u2019 value which is also real. Hence we can define the six trigonometric functions as follows.<\/p>\n

1. f : R \u2192 [-1, 1] defined by f(x) = sin x
\n\"Plus<\/p>\n

2. f : R \u2192 [-1, 1] defined by f(x) = cos x
\n\"Plus<\/p>\n

3. f : R – {n\u03c0, n \u2208 Z} \u2192 R – (-1, 1) defined by f(x) = \\(\\frac{1}{\\sin x}\\) = cosec x
\n\"Plus<\/p>\n

4. f : R – {(2n + 1) \\(\\frac{\\pi}{2}\\)} \u2192 R – (-1, 1) defined by f(x) = \\(\\frac{1}{\\cos x}\\) = sec x
\n\"Plus<\/p>\n

5. f : R – {(2n + 1)\u03c0, n \u2208 Z} \u2192 R defined by f(x) = \\(\\frac{\\sin x}{\\cos x}\\) = tan x
\n\"Plus<\/p>\n

6. f : R – {n\u03c0, n \u2208 Z} \u2192 R defined by f(x) = \\(\\frac{\\cos x}{\\sin x}\\) = cot x
\n\"Plus<\/p>\n

Sign of trigonometric functions in different quadrants;
\n\"Plus
\nFor odd multiple of \\(\\frac{\\pi}{2}\\) trignometric functions changes as given below.
\nsin \u2192 cos
\ncos \u2192 sin
\nsec \u2192 cosec
\ncosec \u2192 sec
\ntan \u2192 cot
\ncot \u2192 tan<\/p>\n

The value of trigonometric functions for some specific angles;
\n\"Plus<\/p>\n

III. Compound Angle Formula<\/span><\/p>\n

sin(x + y) = sin x cos y + cos x sin y<\/p>\n

sin(x – y) = sin x cos y – cos x sin y<\/p>\n

cos(x + y) = cos x cos y – sin x sin y<\/p>\n

cos(x – y) = cos x cos y + sin x sin y
\n\"Plus
\nsin(x + y) sin(x – y) = sin2<\/sup> x – sin2<\/sup> y = cos2<\/sup> x – cos2<\/sup> y<\/p>\n

cos(x + y) cos(x – y) = cos2<\/sup> x – sin2<\/sup> y
\n\"Plus<\/p>\n

IV. Multiple Angle Formula<\/span><\/p>\n

cos2x = cos2<\/sup> x – sin2<\/sup> x
\n= 1 – 2sin2<\/sup> x
\n= 2 cos2<\/sup> x – 1
\n= \\(\\frac{1-\\tan ^{2} x}{1+\\tan ^{2} x}\\)<\/p>\n

\"Plus<\/p>\n

V. Sub-Multiple Angle Formula<\/span>
\n\"Plus<\/p>\n

\"Plus<\/p>\n

VI. Sum Formula<\/span>
\n\"Plus<\/p>\n

VII. Product Formula<\/span><\/p>\n

2 sin x cos y = sin(x + y) + sin(x – y)<\/p>\n

2 cos x sin y = sin(x + y) – sin(x – y)<\/p>\n

2 cos x cos y = cos(x + y) + cos(x – y)<\/p>\n

2 sin x sin y = cos(x – y) – cos(x + y)<\/p>\n

VIII. Solution of Trigonometric Equations<\/span><\/p>\n

sin x = 0 gives x = n\u03c0, where n \u2208 Z<\/p>\n

cos x = 0 gives x = (2n + 1)\u03c0, where n \u2208 Z<\/p>\n

tanx = 0 gives x = n\u03c0, where n \u2208 Z<\/p>\n

sin x = sin y \u21d2 x = n\u03c0 + (-1)n<\/sup> y, where n \u2208 Z<\/p>\n

cos x = cos y \u21d2 x = 2n\u03c0 \u00b1 y, where n \u2208 Z<\/p>\n

tan x = tan y \u21d2 x = n\u03c0 + y, where n \u2208 Z<\/p>\n

Principal solution is the solution which lies in the interval 0 \u2264 x \u2264 2\u03c0.<\/p>\n

IX. Sine and Cosine formulae<\/span><\/p>\n

Let ABC be a triangle. By angle A we mean the angle between the sides AB and AC which lies between 0\u00b0 and 180\u00b0. The angles B and C are similarly defined. The sides AB, BC, and CA opposite to the vertices C, A, and B will be denoted by c, a, and b, respectively.<\/p>\n

Theorem 1 (sine formula): In any triangle, sides are proportional to the sines of the opposite angles. That is, in a triangle ABC
\n\\(\\frac{\\sin A}{a}=\\frac{\\sin B}{b}=\\frac{\\sin C}{c}\\)<\/p>\n

Theorem 2 (Cosine formulae): Let A, B and C be angles of a triangle and a, b and c be lengths of sides opposite to angles A, B, and C, respectively, then
\na2<\/sup> = b2<\/sup> + c2<\/sup> – 2bc cos A
\nb2<\/sup> = c2<\/sup> + a2<\/sup> – 2ca cos B
\nc2<\/sup> = a2<\/sup> + b2<\/sup> – 2ab cos C<\/p>\n

A convenient form of the cosine formulae, when angles are to be found are as follows:
\n\"Plus<\/p>\n

We hope the Plus One Maths Notes Chapter 3 Trigonometric Functions help you. If you have any query regarding Kerala Plus One Maths Notes Chapter 3 Trigonometric Functions, drop a comment below and we will get back to you at the earliest.<\/p>\n","protected":false},"excerpt":{"rendered":"

Plus One Maths Notes Chapter 3 Trigonometric Functions is part of Plus One Maths Notes. Here we have given Kerala Plus One Maths Notes Chapter 3 Trigonometric Functions. Board SCERT, Kerala Text Book NCERT Based Class Plus One Subject Maths Notes Chapter Chapter 3 Chapter Name Trigonometric Functions Category Plus\u00a0One Kerala Kerala Plus One Maths […]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[42728],"tags":[],"yoast_head":"\nPlus One Maths Notes Chapter 3 Trigonometric Functions - A Plus Topper<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aplustopper.com\/plus-one-maths-notes-chapter-3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Plus One Maths Notes Chapter 3 Trigonometric Functions\" \/>\n<meta property=\"og:description\" content=\"Plus One Maths Notes Chapter 3 Trigonometric Functions is part of Plus One Maths Notes. Here we have given Kerala Plus One Maths Notes Chapter 3 Trigonometric Functions. 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