Question

Tính:   a) \(\sin ( - {675^ \circ })\)     b) \(\tan \frac{{15\pi }}{4}\)

Answer 1

Ta có: \(\sin ( - {675^ \circ }) = \sin ({45^ \circ } - {2.360^ \circ }) = \sin {45^ \circ } = \frac{{\sqrt 2 }}{2}\)

\(\tan \frac{{15\pi }}{4} = \tan \left( {3\pi  + \frac{{3\pi }}{4}} \right) = \tan \left( {\pi  + \frac{{3\pi }}{4}} \right) = \tan \left( {\frac{{3\pi }}{4}} \right) = \tan \left( {\pi  - \frac{\pi }{4}} \right) =  - \tan \left( {\frac{\pi }{4}} \right) =  - 1\)