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- Question 3, Exercise 9.1
- ====== Question 3, Exercise 9.1 ====== Solutions of Question 3 of Exercise 9.1 of Unit 09: Trigonometric Fun... (i)===== Find domain and range: $y=7 \cos 4x$ ** Solution. ** AS \begin{align*} & -1\leq \cos 4x \leq 1 \... = Find domain and range: $y=\cos \frac{x}{3}$ ** Solution. ** AS \begin{align*} & -1\leq \cos \frac{x}{3}... Find domain and range: $y=\sin \frac{2 x}{3}$ ** Solution. ** AS \begin{align*} & -1 \leq \sin \frac{2x}{
- Question 5(vi-x), Exercise 9.1
- ====== Question 5(vi-x), Exercise 9.1 ====== Solutions of Question 5(vi-x) of Exercise 9.1 of Unit 09: Trigo... of the function: $y=2 \operatorname{Sin} 3 x$ ** Solution. ** =====Question 5(vi)===== Draw the graph of ... h of the function: $y=3 \operatorname{Cos} x$ ** Solution. ** =====Question 5(vii)===== Draw the graph of... of the function: $y=\operatorname{Cos}^{2} x$ ** Solution. ** =====Question 5(viii)===== Draw the graph o
- Question 6, Exercise 9.1
- ====== Question 6, Exercise 9.1 ====== Solutions of Question 6 of Exercise 9.1 of Unit 09: Trigonometric Fun... 6(i)===== Find the period: $y=6 \sec(2 x-3)$ ** Solution. ** Since period of the $\sec$ is $2\pi$, theref... 6(ii)===== Find the period: $y=\cos (5 x+4)$ ** Solution. ** Since period of the $\cos$ is $2\pi$, theref... d the period: $y=\cot 4 x+\sin \frac{5 x}{2}$ ** Solution. ** FIXME(unable to solve) =====Question 6(iv)==
- Question 10(i-v), Review Exercise
- ====== Question 10(i-v), Review Exercise ====== Solutions of Question 10(i-v) of Review Exercise of Unit 09:... amabad, Pakistan. =====Question 10(i)===== ** Solution. ** =====Question 10(ii)===== ** Solution. ** =====Question 10(iii)===== ** Solution. ** =====Question 10(iv)===== ** Solution. ** =====Qu
- Question 10(vi-x), Review Exercise
- ====== Question 10(vi-x), Review Exercise ====== Solutions of Question 10(vi-x) of Review Exercise of Unit 0... mabad, Pakistan. =====Question 10(vi)===== ** Solution. ** =====Question 10(vii)===== ** Solution. ** =====Question 10(viii)===== ** Solution. ** =====Question 10(ix)===== ** Solution. ** =
- Question 10(xi-xv), Review Exercise
- ====== Question 10(xi-xv), Review Exercise ====== Solutions of Question 10(xi-xv) of Review Exercise of Unit... mabad, Pakistan. =====Question 10(xi)===== ** Solution. ** =====Question 10(xii)===== ** Solution. ** =====Question 10(xiii)===== ** Solution. ** =====Question 10(xiv)===== ** Solution. ** ====
- Question 1, Exercise 9.1
- ====== Question 1, Exercise 9.1 ====== Solutions of Question 1 of Exercise 9.1 of Unit 09: Trigonometric Fun... c function: $y=2-2 \operatorname{Cos} \theta$ ** Solution. ** We know \begin{align*} -1 \leq \operatorname... 2}{3}-\dfrac{1}{2} \operatorname{Sin} \theta$ ** Solution. ** We know \begin{align*} -1 \leq \operatorname... dfrac{1}{5}-2 \operatorname{Sin}(3 \theta-7)$ ** Solution. ** We know \begin{align*} -1 \leq \operatorname
- Question 2, Exercise 9.1
- ====== Question 2, Exercise 9.1 ====== Solutions of Question 2 of Exercise 9.1 of Unit 09: Trigonometric Fun... $y=\dfrac{1}{4+3 \operatorname{Sin} \theta}$ ** Solution. ** We know \begin{align*} -1 \leq \operatorname... {1}{\frac{1}{2}-5 \operatorname{Cos} \theta}$ ** Solution. ** {{ :math-11-nbf:sol:unit09:math-11-nbf-ex9-1... y=\dfrac{1}{\frac{1}{3}-4 \sin (2 \theta-5)}$ ** Solution. ** **Same as Question 2(ii), we see that given
- Question 4(i-iv), Exercise 9.1
- ====== Question 4(i-iv), Exercise 9.1 ====== Solutions of Question 4(i-iv) of Exercise 9.1 of Unit 09: Trigo... ion is odd or even: $y=\sin x+x \cdot \cos x$ ** Solution. ** Consider $f(x)=\sin x+x \cdot \cos x$. Take... or even: $y=x^{3} \cdot \sin x \cdot \cos x$ ** Solution. ** Consider $f(x)=x^{3} \cdot \sin x \cdot \cos... ven: $y=\dfrac{x^{2} \cdot \tan x}{x+\sin x}$ ** Solution. ** Consider \[y = \frac{x^2 \cdot \tan x}{x +
- Question 4(v-viii), Exercise 9.1
- ====== Question 4(v-viii), Exercise 9.1 ====== Solutions of Question 4(v-viii) of Exercise 9.1 of Unit 09: T... dd or even: $y=\dfrac{\sin ^{2} x}{x+\tan x}$ ** Solution. ** Consider \[y = \frac{\sin^2 x}{x + \tan x}\... or even: $y=\dfrac{\tan x-\sin x}{\sin^3 x}$ ** Solution. ** Consider \[y = \frac{\tan x - \sin x}{\sin^... is odd or even: $y=\dfrac{\sec x}{x+\tan x}$ ** Solution. ** Consider \[y = \frac{\tan x - \sin x}{\sin^
- Question 5(i-v), Exercise 9.1
- ====== Question 5(i-v), Exercise 9.1 ====== Solutions of Question 5(i-v) of Exercise 9.1 of Unit 09: Trigono... h of the function: $y=2 \operatorname{Sin} x$ ** Solution. ** =====Question 5(ii)===== Draw the graph of... of the function: $y=2 \operatorname{Cos} 3 x$ ** Solution. ** =====Question 5(iii)===== Draw the graph of... of the function: $y=2 \operatorname{Tan} 2 x$ ** Solution. ** =====Question 5(iv)===== Draw the graph of
- Question 9, Exercise 9.1
- ====== Question 9, Exercise 9.1 ====== Solutions of Question 9 of Exercise 9.1 of Unit 09: Trigonometric Fun... 9(i)===== Solve graphically: $\sin x=\cos x$ ** Solution. ** =====Question 9(ii)===== Solve graphically: $\cos x=x$ ** Solution. ** =====Question 9(iii)===== Solve graphically: $\sin x=x$ ** Solution. ** =====Question 9(iv)===== Solve graphicall
- Question 2 and 3, Review Exercise
- ====== Question 2 and 3, Review Exercise ====== Solutions of Question 2 and 3 of Review Exercise of Unit 09:... cos \theta+ \sin \theta=\sqrt{2} \cos \theta$ ** Solution. ** Given $$\cos \theta -\sin \theta=\sqrt{2}\si... cot x}{\sin x \cos x} = \sec^2 x - \csc^2 x$ ** Solution. ** \begin{align*} LHS & = \dfrac{\tan x - \cot x... {\sec^2 x + \tan^2 x} = \sec^2 x - \tan^2 x$ ** Solution. ** \begin{align*} LHS & = \dfrac{\sec^4 x - \ta
- Question 7 & 8, Exercise 9.1
- ====== Question 7 & 8, Exercise 9.1 ====== Solutions of Question 7 & 8 of Exercise 9.1 of Unit 09: Trigonome... e{Sin} 2 x$ in $[0,2 \pi]$ on the same scale. ** Solution. ** =====Question 8===== Draw the graphs of ... e{Cos} 2 x$ in $[0,2 \pi]$ on the same scale. ** Solution. ** ====Go to ==== <text align="left"><btn
- Question 5 and 6, Review Exercise
- ====== Question 5 and 6, Review Exercise ====== Solutions of Question 5 and 6 of Review Exercise of Unit 09:... Islamabad, Pakistan. =====Question 5===== ** Solution. ** =====Question 6===== ** Solution. ** ====Go to ==== <text align="left"><btn type="primary">