{"id":35003,"date":"2022-08-24T17:37:33","date_gmt":"2022-08-24T12:07:33","guid":{"rendered":"https:\/\/apboardsolutions.guru\/?p=35003"},"modified":"2022-08-24T17:37:33","modified_gmt":"2022-08-24T12:07:33","slug":"inter-1st-year-maths-1a-trigonometric-ratios-up-to-transformations-solutions-ex-6b","status":"publish","type":"post","link":"https:\/\/apboardsolutions.guru\/inter-1st-year-maths-1a-trigonometric-ratios-up-to-transformations-solutions-ex-6b\/","title":{"rendered":"Inter 1st Year Maths 1A Trigonometric Ratios up to Transformations Solutions Ex 6(b)"},"content":{"rendered":"

Practicing the Intermediate 1st Year Maths 1A Textbook Solutions<\/a> Inter 1st Year Maths 1A Trigonometric Ratios up to Transformations Solutions Exercise 6(b) will help students to clear their doubts quickly.<\/p>\n

Intermediate 1st Year Maths 1A Trigonometric Ratios up to Transformations Solutions Exercise 6(b)<\/h2>\n

I. Find the periods for the given 1 – 5 functions.<\/span><\/p>\n

Question 1.
\ncos(3x + 5) + 7
\nSolution:
\nf(x) = cos(3x + 5) + 7
\nWe know that the function g(x) = cos x for all x \u2208 R has the period 2\u03c0.
\nNow f(x) = cos(3x + 5) + 7
\nWe get that f(x) is periodic and the period of f is \\(\\frac{2 \\pi}{|3|}=\\frac{2 \\pi}{3}\\)<\/p>\n

Question 2.
\ntan 5x
\nSolution:
\nThe function g(x) = tan x periodic and \u03c0 is the period.
\n\u2234 f(x) = tan 5x periodic and its period is \\(\\frac{\\pi}{|5|}=\\frac{\\pi}{5}\\)<\/p>\n

\"Inter<\/p>\n

Question 3.
\n\\(\\cos \\left(\\frac{4 x+9}{5}\\right)\\)
\nSolution:
\nThe function h(x) = cos x for all x \u2208 R has the period 2\u03c0.
\nNow f(x) = \\(\\cos \\left(\\frac{4 x}{5}+\\frac{9}{5}\\right)\\) is periodic and period of f is \\(\\frac{2 \\pi}{\\left(\\frac{4}{5}\\right)}=\\frac{5 \\pi}{2}\\)<\/p>\n

Question 4.
\n|sin x|
\nSolution:
\nThe function h(x) = sin x for all x \u2208 R has the period 2\u03c0.
\nBut f(x) = |sin x| is periodic and its period is \u03c0.
\n\u2235 f(x + \u03c0) = |sin(x + \u03c0)|
\n= |-sin x|
\n= sin x<\/p>\n

Question 5.
\ntan(x + 4x + 9x + …… + n2<\/sup>x) (n any positive integer)
\nSolution:
\ntan(12<\/sup> + 22<\/sup> + 32<\/sup> + …… + n2<\/sup>) x = \\(\\tan \\left[\\frac{n(n+1)(2 n+1)}{6}\\right] x\\)
\nperiod = \\(\\frac{6 \\pi}{n(n+1)(2 n+1)}\\)<\/p>\n

Question 6.
\nFind a sine function whose period is \\(\\frac{2}{3}\\)
\nSolution:
\n\\(\\frac{2 \\pi}{|k|}=\\frac{2}{3}\\)
\n3\u03c0 = |k|
\n\u2234 sin kx = sin 3\u03c0x<\/p>\n

\"Inter<\/p>\n

Question 7.
\nFind a cosine function whose period is 7.
\nSolution:
\n\\(\\frac{2 \\pi}{|k|}\\) = 7
\n\\(\\frac{2 \\pi}{7}\\) = |k|
\n\u2234 cos kx = cos \\(\\frac{2 \\pi}{7}\\) x<\/p>\n

II. Sketch the graph of the following functions.<\/span><\/p>\n

Question 1.
\ntan x between 0 and \\(\\frac{\\pi}{4}\\)
\nSolution:
\n\"Inter<\/p>\n

Question 2.
\ncos 2x in [0, \u03c0]
\nSolution:
\n\"Inter<\/p>\n

Question 3.
\nsin 2x in the interval (0, \u03c0)
\nSolution:
\n\"Inter<\/p>\n

\"Inter<\/p>\n

Question 4.
\nsin x in the interval [-\u03c0, +\u03c0]
\nSolution:
\n\"Inter<\/p>\n

Question 5.
\ncos2<\/sup>x in [0, \u03c0]
\nSolution:
\n\"Inter<\/p>\n

III.<\/span><\/p>\n

Question 1.
\nSketch the region enclosed by y = sin x, y = cos x and X-axis in the interval [0, \u03c0].
\nSolution:
\n\"Inter<\/p>\n","protected":false},"excerpt":{"rendered":"

Practicing the Intermediate 1st Year Maths 1A Textbook Solutions Inter 1st Year Maths 1A Trigonometric Ratios up to Transformations Solutions Exercise 6(b) will help students to clear their doubts quickly. Intermediate 1st Year Maths 1A Trigonometric Ratios up to Transformations Solutions Exercise 6(b) I. Find the periods for the given 1 – 5 functions. Question …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[15],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/35003"}],"collection":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/comments?post=35003"}],"version-history":[{"count":1,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/35003\/revisions"}],"predecessor-version":[{"id":35004,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/35003\/revisions\/35004"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/media?parent=35003"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/categories?post=35003"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/tags?post=35003"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}