Bài 3. Tính:
a) \(\sinα\), nếu \(\cos \alpha = {{ - \sqrt 2 } \over 3},{\pi \over 2} < \alpha < \pi \)
b) \(\cosα\), nếu \(\tan \alpha = 2\sqrt 2 ,\pi < \alpha < {{3\pi } \over 2}\)
c) \(\tanα\), nếu \(\sin \alpha = {{ - 2} \over 3},{{3\pi } \over 2} < \alpha < 2\pi \)
d) \(\cotα\), nếu \(\cos \alpha = {{ - 1} \over 4},{\pi \over 2} < \alpha < \pi \)
a) Nếu \({\pi \over 2} < \alpha < \pi \) thì \(\sinα>0\)
\(\sin \alpha = \sqrt {1 - {{\cos }^2}x} = \sqrt {1 - {2 \over 9}} = {{\sqrt 7 } \over 3}\)
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b) Nếu \(\pi < \alpha < {{3\pi } \over 2}\) thì \(\cosα<0\)
\(\cos \alpha = - \sqrt {{1 \over {1 + {{\tan }^2}\alpha }}} = - \sqrt {{1 \over {1 + 8}}} = - {1 \over 3}\)
c) \({{3\pi } \over 2} < \alpha < 2\pi \) thì \(\tan α<0, \cosα>0\)
\(\tan\alpha = {{\sin \alpha } \over {\cos \alpha }} = ( - {2 \over 3}):\sqrt {1 - ({2 \over 3}} {)^2} = - {{2\sqrt 5 } \over 5}\)
d) \({\pi \over 2} < \alpha < \pi \) thì \(\cotα<0, \sinα>0\)
\(\cot \alpha = \left( { - {1 \over 4}} \right):\sqrt {1 - {{\left( {{1 \over 4}} \right)}^2}} = - {{\sqrt {15} } \over 15}\)