Cho \(\pi
a) \(\cos \left( {\alpha + \pi } \right)\);
b) \(\sin \left( {\frac{\pi }{2} - \alpha } \right)\);
c) \(\tan \left( {\alpha + \frac{{3\pi }}{2}} \right)\);
d) \(\cot \left( {\alpha - \frac{\pi }{2}} \right)\);
e) \(\cos \left( {2\alpha + \frac{\pi }{2}} \right)\);
g) \(\sin \left( {\pi - 2\alpha } \right)\).
Sử dụng kiến thức về giá trị lượng giác của các góc lượng giác có liên quan đặc biệt:
a) \(\cos \left( {\pi + \alpha } \right) = - \cos \alpha \)
b) \(\sin \left( {\frac{\pi }{2} - \alpha } \right) = \cos \alpha \)
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c) \(\tan \left( {2\pi + \alpha } \right) = \tan \alpha \), \(\tan \left( { - \alpha } \right) = - \tan \alpha \), \(\tan \left( {\frac{\pi }{2} - \alpha } \right) = \cot \alpha \)
d) \(\cot \left( { - \alpha } \right) = - \cot \alpha \), \(\cot \left( {\frac{\pi }{2} - \alpha } \right) = \tan \alpha \)
e) \(\cos \left( {\pi + \alpha } \right) = - \cos \alpha \), \(\cos \left( { - \alpha } \right) = \cos \alpha \), \(\cos \left( {\frac{\pi }{2} - \alpha } \right) = \sin \alpha \)
g) \(\sin \left( {\pi - \alpha } \right) = \sin \alpha \)
a) \(\cos \left( {\alpha + \pi } \right) \) \( = - \cos \alpha > 0\) vì \(\pi
b) \(\sin \left( {\frac{\pi }{2} - \alpha } \right) \) \( = \cos \alpha
c) \(\tan \left( {\alpha + \frac{{3\pi }}{2}} \right) \) \( = \tan \left( {\alpha + 2\pi - \frac{\pi }{2}} \right) \) \( = - \tan \left( {\frac{\pi }{2} - \alpha } \right) \) \( = - \cot \alpha
d) \(\cot \left( {\alpha - \frac{\pi }{2}} \right) \) \( = - \cot \left( {\frac{\pi }{2} - \alpha } \right) \) \( = - \tan \alpha
e) \(\cos \left( {2\alpha + \frac{\pi }{2}} \right) \) \( = \cos \left( {2\alpha + \pi - \frac{\pi }{2}} \right) \) \( = - \cos \left( {2\alpha - \frac{\pi }{2}} \right) \) \( = - \cos \left( {\frac{\pi }{2} - 2\alpha } \right) \) \( = - \sin 2\alpha
g) \(\sin \left( {\pi - 2\alpha } \right) \) \( = \sin 2\alpha > 0\) vì \(2\pi