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- Question 1, Exercise 9.1 @math-11-nbf:sol:unit09
- ions of Question 1 of Exercise 9.1 of Unit 09: Trigonometric Functions. This is unit of Model Textbook... === Find the maximum and minimum values of the trigonometric function: $y=2-2 \operatorname{Cos} \thet... m value $(M) = 4$ \\ and minimum value $(m) = 0$. GOOD **Alternative Method:** Given: $$y=2-2 \opera... ximum value (M) = 4 \\ and mimimum value (m) = 0. GOOD =====Question 1(ii)===== Find the maximum an
- Question 1, Exercise 1.1 @math-11-nbf:sol:unit01
- because i^2=-1\\ &=i\cdot(-1)\\ &=-i.\end{align} GOOD ====Question 1(ii)==== Evaulate ${{\left( -i... )^{11} \cdot i \\ &=-(-1)\cdot i = i. \end{align} GOOD ====Question 1(iii)==== Evaluate ${{\left( -1 \... =\dfrac{i}{-\left( -1 \right)}\\ &=i\end{align} GOOD ====Question 1(iv)==== Evaluate $\dfrac{2}{(-1)^{\frac{3}{2}}}$. GOOD **Solution.** \begin{align}{{\left( -1 \right
- Question 2, Exercise 1.1 @math-11-nbf:sol:unit01
- +i2)+(2+i4)\\ =&(3+2)+(i2+i4)\\ =&5+i6\end{align} GOOD ====Question 2(ii)==== Write the following com... +3i)-(2+5i)\\ =&(4-2)+(3i-5i)\\ =&2-2i\end{align} GOOD ====Question 2(iii)==== Write the following com... i)+(4-7i)\\ =&(4+4)+(7i-7i)\\ =&8+0i. \end{align} GOOD ====Question 2(iv)==== Write the following com... )-(2-5i)\\ =&(2-2)+(5i+5i)\\ =&0+10i. \end{align} GOOD ====Question 2(v)==== Write the following comp
- Question 1,Review Exercise @math-11-nbf:sol:unit09
- s of Question 1 of Review Exercise of Unit 09: Trigonometric Functions. This is unit of Model Textbook... {1}{2}$</collapse> ii. The exact value of the trigonometric function $\tan (-15 \pi)=$\\ * (a) $ 0$\\... theta=45^{\circ}$, then the value of the given trigonometric identity is:\\ * (a) $\frac{1}{\sqrt{2}}... d="true">(a):$\cos \theta$ </collapse> v. The trigonometric identity $\dfrac{\sin \alpha + \sin 2\alp
- Question 8, Exercise 1.2 @math-11-nbf:sol:unit01
- ies & 4x^2+4y^2-4y-15=0, \end{align} as required. GOOD ====Question 8(ii)==== Write $|z-1|=|\bar{z}+i|... \\ \implies & x - y =0, \end{align} as required. GOOD ====Question 8(iii)==== Write $|z-4 i|+|z+4 i|=... s & 25x^2 + 9y^2 = 225, \end{align} as required. GOOD ====Question 8(iv)==== Write $\frac{1}{2} \oper... } y=4 \\ \implies & y=8, \end{align} as required. GOOD ====Question 8(v)==== Write $lm\left(\dfrac{z-1
- Question 10, Exercise 1.2 @math-11-nbf:sol:unit01
- overline{z_1} \right| = \sqrt{13}.$$ As required. GOOD ====Question 10(ii)==== For $z_{1}=-3+2 i$ and ... ght)} = \frac{\overline{z_1}}{\overline{z_2}}. \] GOOD ====Question 10(iii)==== For $z_{1}=-3+2 i$ an... = \overline{z_1} \overline{z_2}, \] as required. GOOD ====Question 10(iv)==== For $z_{1}=-3+2 i$ and... e{z_1 + z_2} = \overline{z_1} + \overline{z_2}.\] GOOD ====Question 10(v)==== For $z_{1}=-3+2 i$ and $
- Question 3, Exercise 2.1 @math-11-nbf:sol:unit02
- Pakistan. =====Question 3===== Identify the diagonal matrix, scalar matrix, identity matrix, lower ... A: Lower triangular matrix\\ B: Scalar matrix; Diagonal matrix\\ C: Lower triangular matrix\\ D: Identity matrix; Scalar matrix; Diagonal matrix\\ E: Diagonal matrix\\ F: Upper triangular matrix\\ G: Diagonal matrix\\ H: Scalar matrix;
- Question 3(vi, vii, viii, ix & x) Exercise 8.3 @math-11-nbf:sol:unit08
- x) of Exercise 8.3 of Unit 08: Fundamental of Trigonometry. This is unit of Model Textbook of Mathema... = \sec y(\sin 4y - \sin 2y)\\ &= RHS \end{align*} GOOD =====Questio 3(vii)===== Prove the identity $\d... & = \tan 5\beta \cot \beta\\ &= RHS \end{align*} GOOD =====Questio 3(viii)===== Prove the identity $\... ta} \\ & = -2 \cos 2\theta \\ &= RHS \end{align*} GOOD :!: **Correction:**\\ The corrected version of
- Question 2, Exercise 9.1 @math-11-nbf:sol:unit09
- ions of Question 2 of Exercise 9.1 of Unit 09: Trigonometric Functions. This is unit of Model Textbook... e maximum and minimum values of the reciprocal trigonometric function: $y=\dfrac{1}{4+3 \operatorname{... ) = 1$ \\ and minimum value $(m) = \dfrac{1}{7}$. GOOD =====Question 2(ii)===== Find the maximum and minimum values of the reciprocal trigonometric function: $y=\dfrac{1}{\frac{1}{2}-5 \ope
- Question 3, Exercise 1.1 @math-11-nbf:sol:unit01
- -9i}{2}\\ =&\dfrac{7}{2}-\dfrac{9}{2}i\end{align} GOOD ====Question 3(ii)==== Simplify the following $... 25}\\ =&\dfrac{7}{25}-\dfrac{1}{25}i. \end{align} GOOD ====Question 3(iii)==== Simplify the following... \ =&-\dfrac{2}{10}i\\ =&-\dfrac{1}{5}i\end{align} GOOD ====Question 3(iv)==== Simplify the following $... \\ =&\dfrac{1}{2i}-\dfrac{1}{2i}\\ =&0\end{align} GOOD ====Question 3(v)==== Simplify: $(2+i)^2+\dfra
- Question 7, Exercise 1.1 @math-11-nbf:sol:unit01
- rt{265}\end{align} Hence $|11+12 i|=\sqrt{265}$. GOOD ====Question 7(ii)==== Find the magnitude of ... = 3. \end{align} Hence $$|(2+3 i)-(2+6 i)|=3.$$ GOOD ====Question 7(iii)==== Find the magnitude of t... t{5} = 15.\end{align} Hence $|(2-i)(6+3 i)|=15$. GOOD ====Question 7(iv)==== Find the magnitude of th... dfrac{3-2 i}{2+i} \right|=\sqrt{\dfrac{13}{5}}$. GOOD ====Question 7(v)==== Find the magnitude of the
- Question 2, Exercise 8.1 @math-11-nbf:sol:unit08
- n 2 of Exercise 8.1 of Unit 08: Fundamental of Trigonometry. This is unit of Model Textbook of Mathema... \ & = \dfrac{\sqrt{3}+1}{2\sqrt{2}}. \end{align*} GOOD ===== Question 2(b)===== Use the value of... & = -\dfrac{\sqrt{3}+1}{2\sqrt{2}}. \end{align*} GOOD **Alternative Method (if $\cos 15^{\circ}$ is ... & = -\dfrac{\sqrt{3}+1}{2\sqrt{2}}. \end{align*} GOOD ===== Question 2(c)===== Use the value of $\co
- Question 8(xix, xx, xxi & xxii) Exercise 8.2 @math-11-nbf:sol:unit08
- ii) of Exercise 8.2 of Unit 08: Fundamental of Trigonometry. This is unit of Model Textbook of Mathema... cos\alpha}\\ & = \sec\alpha \\ &=RHS \end{align*} GOOD =====Question 8(xx)===== Verify the identi... \frac{\beta}{2} \\ & = 1 \\ & = RHS \end{align*} GOOD =====Question 8(xxi)===== Verify the identi... } \\ & = 2\cos y \sec 2y \\ & = LHS \end{align*} GOOD =====Question 8(xxii)===== Verify the identit
- Question 1(v, vi, vii & viii) Exercise 8.3 @math-11-nbf:sol:unit08
- ii) of Exercise 8.3 of Unit 08: Fundamental of Trigonometry. This is unit of Model Textbook of Mathema... =& \frac{1}{2}[\cos(6u) - \cos(4u) ] \end{align*} GOOD =====Question 1(vi)===== Use the product-to-sum... = \cos 80^{\circ} - \cos 120^{\circ} \end{align*} GOOD :!: =====Question 1(vii)===== Use the product-t... [ \sin 40^{\circ} - \sin 6^{\circ} ] \end{align*} GOOD =====Question 1(viii)===== Use the product-to-
- Question 4, Exercise 1.3 @math-11-nbf:sol:unit01
- 45}{106}i, \omega=\dfrac{2}{53}-\dfrac{7}{53}i.$$ GOOD =====Question 4(ii)===== Solve the simultaneo... \omega = \dfrac{199}{205} + \dfrac{177}{205}i.$$ GOOD =====Question 4(iii)===== Solve the simultaneo... 9}i;\omega= -\dfrac{288}{109}+ \dfrac{88}{109}i$$ GOOD =====Question 4(iv)===== Solve the simultaneou... 1}{53}i; \omega=\dfrac{68}{53}-\dfrac{80}{53}i.$$ GOOD ====Go to ==== <text align="left"><btn type="p