Lanjutan 3 Soal Persiapan Penilaian Tengah Semester Gasal Kelas XI Pendalaman Matematika (Peminatan)

$\begin{array}{ll}\\ 16.&\textrm{Himpunan penyelesaian dari persamaan}\\ &\cos (x-30)^{\circ}= \displaystyle \frac{1}{2}\sqrt{2} \: \: \textrm{untuk}\: \: 0^{\circ}\leq x\leq 360^{\circ}\\ &\textrm{adalah}\: ....\\\\ &\textrm{a}.\quad \displaystyle \left \{ 75^{\circ},285^{\circ} \right \}\\\\ &\textrm{b}.\quad \displaystyle \left \{ 75^{\circ},343^{\circ} \right \}\\\\ &\textrm{c}.\quad \displaystyle \left \{ 75^{\circ},344^{\circ} \right \}\\\\ &\textrm{d}.\quad \displaystyle \color{red}\left \{ 75^{\circ},345^{\circ} \right \}\\\\ &\textrm{e}.\quad \displaystyle \left \{ 75^{\circ},346^{\circ} \right \}\\\\ &\textbf{Jawab}:\\ &\begin{array}{ll}\\ &\begin{aligned} & \cos (x-30)^{\circ}= \displaystyle \frac{1}{2}\sqrt{2} \\ &\cos (x-30)^{\circ}= \cos 45^{\circ}\\ &\Leftrightarrow \: \: x-30^{\circ}=\pm 45^{\circ}+k.360^{\circ}\\ &\Leftrightarrow \quad x =30^{\circ}\pm 45^{\circ}+k.360^{\circ} \\ &k=0\Rightarrow x_{1}=75^{\circ}\: \: (\color{blue}\textrm{mm})\\ &\qquad\textrm{atau}\: \: x_{2}=-15^{\circ}\: \: \color{red}(tm)\\ &k=1\Rightarrow x_{1}=75^{\circ}+360^{\circ} \: \: (\color{red}\textrm{tm})\\ &\qquad \textrm{atau}\: \: \: x_{2}=-15^{\circ}+360^{\circ}=345^{\circ}\: \: \color{blue}(mm) \end{aligned} \\ &\textbf{HP}=\color{red}\color{red}\left \{\displaystyle 75^{\circ},345^{\circ} \right \} \end{array} \end{array}$.

$\begin{array}{ll}\\ 17.&\textrm{Himpunan penyelesaian dari persamaan}\\ &\cos (x-30)^{\circ}= \displaystyle \frac{1}{2}\sqrt{3} \: \: \textrm{untuk}\: \: 0^{\circ}< x< 360^{\circ}\\ &\textrm{adalah}\: ....\\\\ &\textrm{a}.\quad \displaystyle \left \{ 100^{\circ},330^{\circ} \right \}\\\\ &\textrm{b}.\quad \displaystyle \color{red}\left \{ 30^{\circ},330^{\circ} \right \}\\\\ &\textrm{c}.\quad \displaystyle \left \{ 120^{\circ},300^{\circ} \right \}\\\\ &\textrm{d}.\quad \displaystyle \left \{ 60^{\circ},120^{\circ} \right \}\\\\ &\textrm{e}.\quad \displaystyle \left \{ 50^{\circ},300^{\circ} \right \}\\\\ &\textbf{Jawab}:\\ &\begin{array}{ll}\\ &\begin{aligned} & \cos x^{\circ}= \displaystyle \frac{1}{2}\sqrt{3} \\ &\cos x^{\circ}= \cos 30^{\circ}\\ &\Leftrightarrow \quad x =\pm 30^{\circ}+k.360^{\circ} \\ &k=0\Rightarrow x_{1}=30^{\circ}\: \: (\color{blue}\textrm{mm})\\ &\qquad\textrm{atau}\: \: x_{2}=-30^{\circ}\: \: \color{red}(tm)\\ &k=1\Rightarrow x_{1}=30^{\circ}+360^{\circ}=390^{\circ} \: \: (\color{red}\textrm{tm})\\ &\qquad \textrm{atau}\: \: \: x_{2}=-30^{\circ}+360^{\circ}=330^{\circ}\: \: \color{blue}(mm) \end{aligned} \\ &\textbf{HP}=\color{red}\color{red}\left \{\displaystyle 30^{\circ},330^{\circ} \right \} \end{array} \end{array}$