Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
*)\\
- 690^\circ = 30^\circ - 2.360^\circ \\
\Rightarrow \sin \left( { - 690^\circ } \right) = \sin 30^\circ = \dfrac{1}{2}\\
\cos \left( { - 690^\circ } \right) = \cos 30^\circ = \dfrac{{\sqrt 3 }}{2}\\
\tan \left( { - 690^\circ } \right) = \dfrac{{\sin \left( { - 690^\circ } \right)}}{{\cos \left( { - 690^\circ } \right)}} = \dfrac{1}{{\sqrt 3 }}\\
\cot \left( { - 690^\circ } \right) = \dfrac{{\cos \left( { - 690^\circ } \right)}}{{\sin \left( { - 690^\circ } \right)}} = \sqrt 3 \\
*)\\
495^\circ = 135^\circ + 360^\circ \\
\sin 495^\circ = \sin 135^\circ = \sin \left( {180^\circ - 135^\circ } \right) = \sin 45^\circ = \dfrac{{\sqrt 2 }}{2}\\
\cos 495^\circ = \cos 135^\circ = - \cos \left( {180^\circ - 135^\circ } \right) = - \cos 45^\circ = - \dfrac{{\sqrt 2 }}{2}\\
\tan 495^\circ = \dfrac{{\sin 495^\circ }}{{\cos 495^\circ }} = - 1\\
\cot 495^\circ = \dfrac{{\cos 495^\circ }}{{\sin 495^\circ }} = - 1\\
*)\\
- \dfrac{{17\pi }}{3} = - \dfrac{\pi }{3} + 6\pi \\
\Rightarrow \sin \left( { - \dfrac{{17\pi }}{3}} \right) = \sin \left( { - \dfrac{\pi }{3}} \right) = - \sin \dfrac{\pi }{3} = - \dfrac{{\sqrt 3 }}{2}\\
\cos \left( { - \dfrac{{17\pi }}{3}} \right) = \cos \left( { - \dfrac{\pi }{3}} \right) = \cos \dfrac{\pi }{3} = \dfrac{1}{2}\\
\Rightarrow \tan \left( { - \dfrac{{17\pi }}{3}} \right) = - \sqrt 3 \\
\cot \left( { - \dfrac{{17\pi }}{3}} \right) = - \dfrac{1}{{\sqrt 3 }}\\
*)\\
\dfrac{{15\pi }}{2} = - \dfrac{\pi }{2} + 8\pi \\
\sin \dfrac{{15\pi }}{2} = \sin \left( { - \dfrac{\pi }{2}} \right) = - \sin \dfrac{\pi }{2} = - 1\\
\cos \left( {\dfrac{{15\pi }}{2}} \right) = \cos \left( { - \dfrac{\pi }{2}} \right) = 0\\
\Rightarrow \cot \dfrac{{15\pi }}{2} = 0
\end{array}\)
