جواب تمرین صفحه 109 درس 4 حسابان یازدهم (مثلثات)

الف

ب

پ

الف

ب

پ

الف

\(\left\{ \begin{array}{l}{y_{Max}} = 1 \Rightarrow \left( {\frac{{4\pi }}{3}\;,\;1} \right)\\{y_{Min}} = - 1 \Rightarrow \left( {\frac{\pi }{3}\;,\; - 1} \right)\end{array} \right.\)

ب

\(\left\{ \begin{array}{l}{y_{Max}} = 0 \Rightarrow \left\{ {\left( {\frac{\pi }{3}\;,\;0} \right)\;,\;\left( {\frac{{7\pi }}{3}\;,\;0} \right)} \right\}\\{y_{Min}} = - 2 \Rightarrow \left( {\frac{{4\pi }}{3}\;,\; - 2} \right)\end{array} \right.\)

پ

\(\left\{ \begin{array}{l}{y_{Max}} = 2 \Rightarrow \left\{ {\left( {0\;,\;2} \right)\;,\;\left( {\pi \;,\;2} \right)\;,\;\left( {2\pi \;,\;2} \right)} \right\}\\{y_{Min}} = 0 \Rightarrow \left\{ {\left( {\frac{\pi }{2}\;,\;1} \right)\;,\;\left( {\frac{{3\pi }}{2}\;,\;1} \right)\;} \right\}\end{array} \right.\)

 اگر بازه بین \(\left[ {0\;,\;\pi } \right]\) که هیچ کدام از نمودارها؛ ولی اگر بازه مورد نظر سوال \(\left[ {\frac{\pi }{3}\;,\;\pi } \right]\)  بوده باشد، نمودار (ب).

الف

\(\begin{array}{l}{h_1} = 50\\{h_2} = 100\sin \theta \\{h_3} = 53\sin \alpha \\H = {h_1} + {h_2} + {h_3} = 50 + 100\sin \theta + 53\sin \alpha \end{array}\)

ب

\(\begin{array}{l}H = 50 + 100\sin \theta + 53\sin \alpha \\23/5 = 50 + 100\sin \theta + 53\sin \left( { - {{30}^ \circ }} \right)\\ \Rightarrow 23/5 = 50 + 100\sin \theta - 26/5\\ \Rightarrow 100\sin \theta = 0\mathop \Rightarrow \limits^{0 \le \theta \le \frac{\pi }{2}} \theta = {0^ \circ }\end{array}\)