Tiêu đề 6. Trigonometric Ratios CQ & MCQ Practice Sheet Solution [HSC 26].pdf ✅

2  Higher Math 1st Paper Chapter-6 GLv‡b, AOC = ABC = 45 OAC Gi †ÿÎdj = 1 2 OA.OCsin45 = 1 2  402  1 2 = 565.685 eM© †m.wg.  OABC i¤^‡mi †ÿÎdj = 2  OAC = 2  565.685 = 1131.37 eM© †m.wg. OAC e„ËKjvi †ÿÎdj wbY©q:  = 45 = 45   180 =  4 †iwWqvb Ges r = 40 †m.wg.  e„ËKjvi †ÿÎdj = 1 2 r 2  = 1 2 (40)2 .  4 = 200 eM© GKK  Qvqv‡Niv As‡ki †ÿÎdj = (1131.37 – 200) = 503.05 eM© GKK (cÖvq) (Ans.) (M) †`Iqv Av‡Q, f(x) = sinx  y = f     2 – 2x = sin     2 – 2x = cos2x  y = cos2x; –  ≤ x ≤  x Gi wewfbœ gv‡bi Rb ̈ y = cos2x Gi gvb `yB `kwgK ̄’vb ch©šÍ wbY©q Kwi: x 0   12   6   4   3  5 12   2  7 12 y 1 0.87 0.5 0 – 0.5 – 0.87 – 1 – 0.87 x  2 3  3 4  5 6  11 12   y – 0.5 0 0.5 0.87 1 † ̄‹j wba©viY: x Aÿ eivei ÿz`aZg e‡M©i 2 evû =  12 y Aÿ eivei ÿz`aZg e‡M©i 10 evû = 1 0 –  6 –  3 –  2 – 2 3 – 5 6 –   6  3  2 2 3 5 6  1 0.5 0 – 0.5 – 1 we›`y ̧‡jv‡K QK KvM‡R ̄’vcb Kwi Ges †hvM Kwi| Gfv‡eB y = cos2x Gi †jLwPÎ cÖ`Ë mxgvq Aw1⁄4Z nj| •ewkó ̈: (i) †jLwPÎwU g~j we›`yMvgx bq| (ii) †jLwPÎwU Awew”Qbœ Ges †XD AvK...wZi (iii) †jLwPÎ †_‡K †`Lv hvq †h, cos2x Gi m‡e©v”P gvb 1 Ges me©wb¤œ gvb – 1 3| `„k ̈Kí-1: A K‡jR †_‡K GKRb mvB‡Kj Av‡ivnx B K‡j‡R †cuŠQvj| K‡jR `yBwU c„w_exi †K‡›`a 18 †KvY Drcbœ K‡i| c„w_exi e ̈vmva© 6440 km. `„k ̈Kí-2: f(x) = sinx [h. †ev. 19] (K) cot 3x 2 dvsk‡bi ch©vq wbY©q Ki| (L) K‡jR `yBwUi ga ̈eZ©x `~iZ¡ wbY©q Ki| (M) y = f(2x) ; –   x   Gi †jLwPÎ A1⁄4b Ki| mgvavb: (K) cot 3x 2 dvsk‡bi ch©vq =  |Pj‡Ki mnM| =  3 2 = 2 3 (Ans.) (L) †K‡›`a Drcbœ †KvY,  = 18 =     18 60   180 †iwWqvb =  600 †iwWqvb e ̈vmva©, r = 6440 wK‡jvwgUvi  K‡jR `yBwUi g‡a ̈eZ©x `~iZ¡, S = r = 6440   600 = 33.72 (cÖvq)  wb‡Y©q `~iZ¡ 33.72 wK‡jvwgUvi| (Ans.) (M) GLv‡b, f(x) = sinx  y = f(2x) = sin2x; –  ≤ x ≤  x –  – 11 12 – 5 6 – 3 4 – 2 3 – 7 12 –  2 – 5 12 y 0 0.5 0.87 1 0.87 0.5 0 – 0.5 x –  3 –  4 –  6 –  12 0  12  6  4 y – 0.87 – 1 – 0.87 – 0.5 0 0.5 0.87 1 x  3 5 12  2 7 12 2 3 3 4 5 6 11 12 y 0.87 0.5 0 – 0.5 – 0.87 – 1 – 0.87 – 0.5 x  y 0 † ̄‹j wba©viY: x Aÿ eivei ÿz`aZg e‡M©i 2 evû =  12 y Aÿ eivei ÿz`aZg e‡M©i 10 evû = 1 0 –  6 –  3 –  2 – 2 3 – 5 6 –   6  3  2 2 3 5 6  1 0.5 0 – 0.5 – 1