Merging man & maths https://www.mathcity.org/ Thu, 04 Jun 2026 17:28:42 +0000 FeedCreator 1.8 https://www.mathcity.org/_media/logo.svg https://www.mathcity.org/ https://www.mathcity.org/math-11-nbf/sol/unit09/re-ex-p1 Question 1,Review Exercise Solutions of Question 1 of Review Exercise of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $\cos \theta=\frac{\sqrt{3}}{2}$$\sin \theta=$$\frac{1}{2}$$-\frac{1}{2}$$\sqrt{3}$$-\frac{2}{\sqrt{3}}$$-\frac{1}{2}$$\tan (-15 \pi)=$$ 0$$-1$$1$$0$$2 \sin \theta+\frac{1}{2}cosec \theta \theta $$\theta=45^{\circ}$$\frac{1}{\sqrt{2}}$$\frac… anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:18 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09/ex9-1-p1 Question 1, Exercise 9.1 Solutions of Question 1 of Exercise 9.1 of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $y=2-2 \operatorname{Cos} \theta$\begin{align*} -1 \leq \operatorname{Cos} \theta \leq 1 \end{align*}$-2$\begin{align*} & 2 \geq -2 \operatorname{Cos} \theta \geq -2 \end{align*}$2$\begin{align*} & 4 \geq 2-2 \operatorname{Cos} \theta \geq 0 \\ … anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:09 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09/ex9-1-p2 Question 2, Exercise 9.1 Solutions of Question 2 of Exercise 9.1 of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $y=\dfrac{1}{4+3 \operatorname{Sin} \theta}$\begin{align*} -1 \leq \operatorname{Sin} \theta \leq 1 \end{align*}$3$\begin{align*} -3 \leq 3 \operatorname{Sin} \theta \leq 3 \end{align*}$4$\begin{align*} & 1 \leq 4+3 \operatorname{Sin} \theta \l… anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:10 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09 Unit 09: Trigonometric Functions This is a ninth unit of the book “Model Textbook of Mathematics for Class XI” published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. On this page we have provided the solutions of the questions.$a+b \sin \theta$$a+b \cos \theta$$a+b \sin(c \theta+d)$$a+b \cos(c \theta+d)$$a, b, c$$d$$\sin \theta$$\cos \theta$$\tan \theta$ anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:25 +0000 https://www.mathcity.org/math-11-nbf/sol/unit08/re-ex-p3 Question 3, Review Exercise Solutions of Question 3 of Review Exercise of Unit 08: Fundamental of Trigonometry. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $\frac{1}{\sqrt{2}}(\sin \beta+\cos \beta)$\begin{align*} &\frac{1}{\sqrt{2}}(\sin \beta+\cos \beta)\\ =& \sin \frac{\pi}{4}\sin \beta+\cos \frac{\pi}{4}\cos \beta\\ =& \cos(\beta -\frac{\pi}{4}) \end{align*}$\frac{1}{\sqrt{2}} \sin 75^… anonymous@undisclosed.example.com (Anonymous) Sat, 09 Nov 2024 18:32:33 +0000 https://www.mathcity.org/math-11-nbf/sol/unit08 Unit 08: Fundamental of Trigonometry [Unit 08: Fundamental of Trigonometry] This is a eight unit of the book “Model Textbook of Mathematics for Class XI” published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. On this page we have provided the solutions of the questions.$\cos(\alpha -\beta)=\cos \alpha \cos\beta+\sin\alpha \sin\beta$$\cos(\alpha +\beta)=\cos \alpha \cos\beta-\sin\alpha \sin\beta$$\sin(\alpha \pm \beta)=\sin \alpha \cos\beta \pm \sin\alpha \co… anonymous@undisclosed.example.com (Anonymous) Sat, 09 Nov 2024 18:51:30 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09/ex9-1-p3 Question 3, Exercise 9.1 Solutions of Question 3 of Exercise 9.1 of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $y=7 \cos 4x$\begin{align*} & -1\leq \cos 4x \leq 1 \,\, \forall \,\, x\in \mathbb{R} \\ \implies & -7\leq 7 \cos 4x \leq 7 \\ \end{align*}$= ]-\infty, \infty[ = \mathbb{R}$$=[-7,7]$$y=\cos \frac{x}{3}$\begin{align*} & -1\leq \cos \frac{x}{3} \… anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:11 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09/ex9-1-p4 Question 4(i-iv), Exercise 9.1 Solutions of Question 4(i-iv) of Exercise 9.1 of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $y=\sin x+x \cdot \cos x$$f(x)=\sin x+x \cdot \cos x$\begin{align*} f(-x) = \sin (-x) + (-x)\cdot \cos (-x) \end{align*}$\sin(-x)=-\sin x$$\cos (-x) = \cos x$\begin{align*} f(x) & = -\sin x - x \cdot \cos x \\ & = -(\sin x + x \cdot … anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:11 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09/ex9-1-p5 Question 4(v-viii), Exercise 9.1 Solutions of Question 4(v-viii) of Exercise 9.1 of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $y=\dfrac{\sin ^{2} x}{x+\tan x}$\[y = \frac{\sin^2 x}{x + \tan x}\]\begin{align*} y(-x) &= \frac{\big(-\sin x\big)^2}{-x - \tan x} \\ &= \frac{\sin^2 x}{-x - \tan x}\\ & = \frac{\sin^2 x}{-(x + \tan x)}\\ & = -\frac{\sin^2 x}{x +… anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:12 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09/ex9-1-p6 Question 5(i-v), Exercise 9.1 Solutions of Question 5(i-v) of Exercise 9.1 of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $y=2 \operatorname{Sin} x$$y=2 \operatorname{Cos} 3 x$$y=2 \operatorname{Tan} 2 x$$\mathrm{y}=\operatorname{Cos} \frac{\mathrm{x}}{2}$ anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:13 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09/ex9-1-p7 Question 5(vi-x), Exercise 9.1 Solutions of Question 5(vi-x) of Exercise 9.1 of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $y=2 \operatorname{Sin} 3 x$$y=3 \operatorname{Cos} x$$y=\operatorname{Cos}^{2} x$$y=\operatorname{Sin}^{2} x$$y=\operatorname{Tan}^{2} x$$y=\operatorname{Sin} \frac{x}{2}$ anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:14 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09/ex9-1-p8 Question 6, Exercise 9.1 Solutions of Question 6 of Exercise 9.1 of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $y=6 \sec(2 x-3)$$\sec$$2\pi$\begin{align*} 6 \sec(2 x-3) & = 6 \sec(2 x-3+2\pi) \\ & = 6 \sec(2(x+\pi)-3) \end{align*}$6 \sec(2 x-3)$$\pi$$y=\cos (5 x+4)$$\cos$$2\pi$\begin{align*} \cos (5 x+4) & = 6 \cos(5x+4+2\pi) \\ & = \cos\left(5\left(x+\fr… anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:15 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09/ex9-1-p9 Question 7 & 8, Exercise 9.1 Solutions of Question 7 & 8 of Exercise 9.1 of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $y=\operatorname{Sin} x$$y=\operatorname{Sin} 2 x$$[0,2 \pi]$$y=\operatorname{Cos} x$$y=\operatorname{Cos} 2 x$$[0,2 \pi]$ anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:15 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09/ex9-1-p10 Question 9, Exercise 9.1 Solutions of Question 9 of Exercise 9.1 of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $\sin x=\cos x$$\cos x=x$$\sin x=x$$\tan x=x$ anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:09 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09/ex9-1-p11 Question 10, Exercise 9.1 Solutions of Question 10 of Exercise 9.1 of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $ V(t)=a \operatorname{Sin}(k(t-d))+c$$56 \mathrm{~Hz} A C$$k$ anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:10 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09/re-ex-1-p2 Question 2 and 3,Review Exercise Solutions of Question 2 and 3 of Review Exercise of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:17 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09/re-ex-1-p3 Question 4, Review Exercise Solutions of Question 4 of Review Exercise of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:18 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09/re-ex-p2 Question 2 and 3, Review Exercise Solutions of Question 2 and 3 of Review Exercise of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $\cos \theta -\sin \theta=\sqrt{2}\sin \theta,$$\cos \theta+ \sin \theta=\sqrt{2} \cos \theta$$$\cos \theta -\sin \theta=\sqrt{2}\sin \theta$$\begin{align*} & \cos \theta=\sqrt{2}\sin \theta + \sin \theta \\ \implies & \cos \the… anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 16:04:15 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09/re-ex-p3 Question 4, Review Exercise Solutions of Question 4 of Review Exercise of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:20 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09/re-ex-p4 Question 5 and 6, Review Exercise Solutions of Question 5 and 6 of Review Exercise of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:22 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09/re-ex-p5 Question 7, Review Exercise Solutions of Question 7 of Review Exercise of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:22 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09/re-ex-p6 Question 8, Review Exercise Solutions of Question 8 of Review Exercise of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:23 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09/re-ex-p7 Question 9, Review Exercise Solutions of Question 9 of Review Exercise of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:23 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09/re-ex-p8 Question 10(i-v), Review Exercise Solutions of Question 10(i-v) of Review Exercise of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:24 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09/re-ex-p9 Question 10(vi-x), Review Exercise Solutions of Question 10(vi-x) of Review Exercise of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:24 +0000 https://www.mathcity.org/math-11-nbf/sol/unit09/re-ex-p10 Question 10(xi-xv), Review Exercise Solutions of Question 10(xi-xv) of Review Exercise of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. anonymous@undisclosed.example.com (Anonymous) Wed, 27 Nov 2024 15:59:19 +0000