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- Question 9, Exercise 8.1
- 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(\
- Question 5 and 6, Exercise 8.1
- 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
- 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 4 Exercise 8.2
- = \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 3(vi, vii, viii, ix & x) Exercise 8.3
- ====== 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 8(xvi, xvii & xviii) Exercise 8.2
- ====== 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
- ====== 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
- ====== 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
- ====== 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
- ====== 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
- Question 3(xi, xii & xiii) Exercise 8.3
- ====== Question 3(xi, xii & xiii) Exercise 8.3 ====== Solutions of Question 3(xi, xii & xiii) of Exercise 8.3 of Unit 08: Fundamental of Trigonometry. This is unit of Model Textbook of Ma
- Question 8(vii, viii & ix) Exercise 8.2
- ====== Question 8(vii, viii & ix) Exercise 8.2 ====== Solutions of Question 8(vii, viii & ix) of Exercise 8.2 of Unit 08: Fundamental of Trigonometry. This is unit of Model Textbook o
- Question 8(i, ii & iii) Exercise 8.2
- ====== Question 8(i, ii & iii) Exercise 8.2 ====== Solutions of Question 8(i, ii & iii) of Exercise 8.2 of Unit 08: Fundamental of Trigonometry. This is unit of Model Textbook of Mat
- Question 8(x, xi & xii) Exercise 8.2
- ====== Question 8(x, xi & xii) Exercise 8.2 ====== Solutions of Question 8(x, xi & xii) of Exercise 8.2 of Unit 08: Fundamental of Trigo... &= \cos2 x\\ &=RHS \end{align*} =====Question 8(xii)===== Verify the identities: $\tan \frac{\beta}{2... ">[[math-11-nbf:sol:unit08:ex8-2-p8|< Question 8(vii, viii & ix) ]]</btn></text> <text align="right"><
- Question 8(xiii, xiv & xv) Exercise 8.2
- ====== Question 8(xiii, xiv & xv) Exercise 8.2 ====== Solutions of Question 8(xiii, xiv & xv) of Exercise 8.2 of Unit 08: Fundamenta... k Board, Islamabad, Pakistan. =====Question 8(xiii)===== Verify the identities: $\csc 2 \alpha-\cot ... -11-nbf:sol:unit08:ex8-2-p9|< Question 8(x, xi & xii) ]]</btn></text> <text align="right"><btn type="s