جواب تمرین صفحه 104 درس 4 حسابان یازدهم (مثلثات)

الف

\(\sin \left( {{{300}^\circ }} \right) = \sin \left( {{{360}^ \circ } - {{60}^ \circ }} \right) = - \sin {60^ \circ } = - \frac{{\sqrt 3 }}{2}\)

ب

\(\cot \left( {{{750}^\circ }} \right) = \cot \left( {{{720}^ \circ } + {{30}^ \circ }} \right) = \cot {30^ \circ } = \sqrt 3 \)

پ

\(\cos \left( { - \frac{\pi }{6}} \right) = \cos \frac{\pi }{6} = \frac{{\sqrt 3 }}{2}\)

ت

\(\cos \left( { - \frac{{23\pi }}{4}} \right) = \cos \left( { - 6\pi + \frac{\pi }{4}} \right) = \cos \frac{\pi }{4} = \frac{{\sqrt 2 }}{2}\)

ث

\(\sin \left( {\frac{{5\pi }}{4}} \right) = \sin \left( {\pi + \frac{\pi }{4}} \right) = - \sin \frac{\pi }{4} = - \frac{{\sqrt 2 }}{2}\)

ج

\(\tan \left( { - {{840}^\circ }} \right) = \tan \left( { - {{720}^ \circ } - {{120}^ \circ }} \right) = \tan \left( { - {{120}^ \circ }} \right) = - \tan \left( {{{90}^ \circ } + {{30}^ \circ }} \right) = \cot {30^ \circ } = \sqrt 3 \)

چ

\(\tan \left( { - {{150}^\circ }} \right) = - \tan \left( {{{180}^ \circ } - {{30}^ \circ }} \right) = \tan \left( {{{30}^ \circ }} \right) = \frac{{\sqrt 3 }}{3}\)

ح

\(\cos \left( {\frac{{9\pi }}{4}} \right) = \cos \left( {2\pi + \frac{\pi }{4}} \right) = \cos \frac{\pi }{4} = \frac{{\sqrt 2 }}{2}\)

خ

\(\tan \left( {\frac{{10\pi }}{3}} \right) = \tan \left( {2\pi + \pi + \frac{\pi }{3}} \right) = \tan \left( {\pi + \frac{\pi }{3}} \right) = - \tan \frac{\pi }{3} = - \;\sqrt 3 \)

الف

\(I = k\sin \left( {\frac{\pi }{2} - \alpha } \right) = k\cos \alpha = k\sin \theta \)

ب

\(I = k\sin \theta \Rightarrow \left\{ \begin{array}{l}\theta = 0 \to I = 0\\\theta = \frac{\pi }{6} \to I = \frac{k}{2}\\\theta = \frac{\pi }{3} \to I = \frac{{\sqrt 3 }}{2}k\end{array} \right.\)

پ

\(I = k\,\,\,\,\,\mathop \Rightarrow \limits^{I = k\sin \theta } \,\,\,\,\,\sin \theta = 1 = \sin \frac{\pi }{2} \Rightarrow \theta = \frac{\pi }{2}\)

الف

درست

ب

نادرست

ج

درست

د

درست