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- Question 9, Exercise 8.1 @math-11-nbf:sol:unit08
- rt{2}}$, $\alpha$ is obtuse angle, i.e. it is in QII.\\ $\cos \beta=-\dfrac{3}{5}$, $\beta$ is obtuse angle, i.e. it is in QII.\\ We have an identity: $$\cos \alpha=\pm \sqrt{1-\sin^2\alpha}.$$ As $\alpha$ lies in QII and $\cos$ is -ive in QII, \begin{align*} \cos\alpha &=-\sqrt{1-\sin^2\alpha}\\ &=-\sqrt{1-{{\left(\
- Unit 08: Fundamental of Trigonometry @math-11-nbf:sol
- * [[math-11-nbf:sol:unit08:ex8-2-p6|Question 8(1, ii & iii) ]] * [[math-11-nbf:sol:unit08:ex8-2-p7|Question 8(iv, v & vi) ]] * [[math-11-nbf:sol:unit08:ex8-2-p8|Question 8(vii, viii & ix) ]] * [[math-11-nbf:sol:unit08:ex8-2-p9|Question 8(x, xi & xii) ]] * [[math-11-nbf:sol
- Question 5 and 6, Exercise 8.1 @math-11-nbf:sol:unit08
- dfrac{5}{12}$ with terminal side of an angles in QII, find $\cos (\alpha+\beta)$ and $\cos (\alpha-\be... iven: $\sin \alpha=\dfrac{4}{5}$, $\alpha$ is in QII and $\tan \beta=-\dfrac{5}{12}$, $\beta$ is in QII. We have an identity: $$\cos \alpha=\pm \sqrt{1-\sin^2\alpha}.$$ As $\alpha$ lies in QII and $\cos$ is -ive in QII, \begin{align*}\cos\alp
- Question 5 Exercise 8.2 @math-11-nbf:sol:unit08
- iven: $\sin 2 \theta=\frac{24}{25}, 2 \theta$ in QII ** Solution. ** Given: $\sin 2\theta=\dfrac{24}{25}$, $2\theta$ in QII. We have $$\cos 2\theta = \pm \sqrt{1-\sin^2 2\theta}$$ Since $2\theta$ in QII, therefore $\cos 2\theta$ is negative. \begin{al... ta=\frac{4}{3}} \end{align*} GOOD =====Question 5(ii)===== Find exact values for $\sin \theta, \cos \t
- Question 10, Exercise 1.2 @math-11-nbf:sol:unit01
- = \sqrt{13}.$$ As required. GOOD ====Question 10(ii)==== For $z_{1}=-3+2 i$ and $z_{2}=1-3 i$ verify:... ne{z_2}} = -\frac{9}{10} + \frac{7}{10}i.\,\, -- (ii)$$ From (i) and (ii), we have \[ \overline{\left( \frac{z_1}{z_2} \right)} = \frac{\overline{z_1}}{\overline{z_2}}. \] GOOD ====Question 10(iii)==== For $z_{1}=-3+2 i$ and $z_{2}=1-3 i$ verify:
- Question 4 Exercise 8.2 @math-11-nbf:sol:unit08
- = \frac{1}{2}} \end{align*} GOOD =====Question 4(ii)===== Find (a) $\sin 2 \theta$ (b) $\cos 2 \theta... ta < \frac{3\pi}{2}\), i.e., \(\theta\) lies in QIII. We have: \begin{align*} \sec \theta &= \pm \sq... \pm \frac{13}{5}\end{align*} \(\theta\) lies in QIII, therefore $\sec \theta <o$\\ \begin{align*}\sec ... \pi}{4}\), that is, \(\frac{\theta}{2}\) lies in QII, thus \(\sin\left(\frac{\theta}{2}\right) > 0\).
- Question 1, Exercise 2.6 @math-11-nbf:sol:unit02
- {3}=0\cdots (i)\\ &x_{1}-2 x_{2}+3 x_{3}=0\cdots (ii)\\ &4 x_{1}+x_{2}-6 x_{3}=0\cdots (iii)\\ \end{align*} For system of equation, \begin{align*} A &= \... m has non-trivial solution. \text{By}\quad(i)-2(ii), we have \begin{align*} &\begin{array}{cccc} 2x_... =2x_3\\ \end{align*} Put the value of $x_3$ in (iii), we have \begin{align*} &4 x_{1}+2x_{3}-6 x_{3}=
- Question 3(vi, vii, viii, ix & x) Exercise 8.3 @math-11-nbf:sol:unit08
- ====== Question 3(vi, vii, viii, ix & x) Exercise 8.3 ====== Solutions of Question 3(vi, vii, viii, ix & x) of Exercise 8.3 of Unit 08: Fundamental of Trigonometry. This is unit of Model Textboo
- Question 1,Review Exercise @math-11-nbf:sol:unit09
- sqrt{3}}{2}$ and the terminal arm of angle is in III quadrant. Then $\sin \theta=$\\ * $\frac{1}... lapsed="true">%%(b)%%: $-\frac{1}{2}$</collapse> ii. The exact value of the trigonometric function $\... se id="a2" collapsed="true">(a): $0$</collapse> iii. If $2 \sin \theta+\frac{1}{2}cosec \theta \theta... apsed="true">(a): $\cos 4x-\cos 10x$</collapse> vii. Express $\sin 5x+\sin 7x$ as a product:\\ * (a)
- Question 2, Exercise 2.6 @math-11-nbf:sol:unit02
- _{3}=0 \cdots(i)\\ &2 x_{1}+3 x_{2}-x_{3}=0\cdots(ii)\\ &3 x_{1}-2 x_{2}+4 x_{3}=0\cdots(iii)\\ \end{align*} Homogenous system has non-trivial solution, i... \ x_3 \end{array} \right]$ =====Question 2(ii)===== Find the value of $\lambda$ for which the s... i)}\\ &2 x_{1}+\lambda x_{2}+x_{3}=0 \quad \text{(ii)}\\ &x_{1}-2 x_{2}+\lambda x_{3}=0 \quad \text{(i
- Question 8(xvi, xvii & xviii) Exercise 8.2 @math-11-nbf:sol:unit08
- ====== Question 8(xvi, xvii & xviii) Exercise 8.2 ====== Solutions of Question 8(xvi, xvii & xviii) of Exercise 8.2 of Unit 08: Fundamental of Trigonometry. This is unit of Model Textbook of M
- Question 1(i, ii, iii & iv) Exercise 8.3 @math-11-nbf:sol:unit08
- ====== Question 1(i, ii, iii & iv) Exercise 8.3 ====== Solutions of Question 1(i, ii, iii & iv) of Exercise 8.3 of Unit 08: Fundamental of Trigonometry. This is unit of Model Textbook of
- Question 1(v, vi, vii & viii) Exercise 8.3 @math-11-nbf:sol:unit08
- ====== Question 1(v, vi, vii & viii) Exercise 8.3 ====== Solutions of Question 1(v, vi, vii & viii) of Exercise 8.3 of Unit 08: Fundamental of Trigonometry. This is unit of Model Textbook of Ma
- Question 2(i, ii, iii, iv and v) Exercise 8.3 @math-11-nbf:sol:unit08
- ====== Question 2(i, ii, iii, iv and v) Exercise 8.3 ====== Solutions of Question 2(i, ii, iii, iv and v) of Exercise 8.3 of Unit 08: Fundamental of Trigonometry. This is unit of Model Textbo
- Question 3(i, ii, iii, iv & v) Exercise 8.3 @math-11-nbf:sol:unit08
- ====== Question 3(i, ii, iii, iv & v) Exercise 8.3 ====== Solutions of Question 3(i, ii, iii, iv & v) of Exercise 8.3 of Unit 08: Fundamental of Trigonometry. This is unit of Model Textbook