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Bài 5. Không sử dụng máy tính, hãy tính:
a) \(\cos {{22\pi } \over 3}\)
b) \(\sin {{23\pi } \over 4}\)
c) \(\sin {{25\pi } \over 3} – \tan {{10\pi } \over 3}\)
d) \({\cos ^2}{\pi \over 8} – {\sin ^2}{\pi \over 8}\)
a) \(\cos {{22\pi } \over 3} = \cos (8\pi – {{2\pi } \over 3})\)
\(= \cos ( – {{2\pi } \over 3}) = \cos ({{2\pi } \over 3}) \)
\(= – \cos {\pi \over 3} = {{ – 1} \over 2}\)
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b) \(\sin {{23\pi } \over 4} = \sin (6\pi – {\pi \over 4})\)
\(= \sin ( – {\pi \over 4}) = – \sin ({\pi \over 4}) = – {{\sqrt 2 } \over 2}\)
c)
\(\eqalign{
& \sin {{25\pi } \over 3} – \tan {{10\pi } \over 3} = \sin (8\pi + {\pi \over 3}) – \tan (3\pi + {\pi \over 3}) \cr
& = sin{\pi \over 3} – \tan {\pi \over 3} = {{\sqrt 3 } \over 2} – \sqrt 3 = {{ – \sqrt 3 } \over 2} \cr} \)
d) \({\cos ^2}{\pi \over 8} – {\sin ^2}{\pi \over 8} = \cos {\pi \over 4} = {{\sqrt 2 } \over 2}\)