Câu 3: trang 155 sgk Đại số 10
Tính:
a) \(sin\,α,\)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 \(\cos \alpha = {{ - 1} \over 4},{\pi \over 2} < \alpha < \pi \)
Bài Làm:
a. \({\pi \over 2} < \alpha < \pi \Rightarrow \sinα>0\)
Ta có: \(\sin \alpha = \sqrt {1 - {{\cos }^2}x} = \sqrt {1 - {2 \over 9}} = {{\sqrt 7 } \over 3}\)
b) \(\pi < \alpha < {{3\pi } \over 2}\Rightarrow \cosα<0\)
Ta có: \(\cos \alpha = - \sqrt {{1 \over {1 + {{\tan }^2}\alpha }}} = - \sqrt {{1 \over {1 + 8}}} = - {1 \over 3}\)
c) \({{3\pi } \over 2} < \alpha < 2\pi \Rightarrow \tan α<0, \cosα>0\)
Ta có \(\tan\alpha = {{\sin \alpha } \over {\cos \alpha }} = \left ( - {2 \over 3} \right )\div \sqrt {1 - \left ( {2 \over 3} \right )^2} = - {{2\sqrt 5 } \over 5}\)
d) \({\pi \over 2} < \alpha < \pi \Rightarrow \cotα<0, \sinα>0\)
Ta có \(\cot \alpha = \left( { - {1 \over 4}} \right):\sqrt {1 - {{\left( {{1 \over 4}} \right)}^2}} = - {{\sqrt {15} } \over 15}\)