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1) а) y = ctg x б) x ≠ πk, k ∈ Z в) y ∈ (-∞; +∞) г) нечётная д) T = π 2) cos 49°48' = 0,6455 3) а) sin 111°·cos21° - sin 21°·cos111° = sin (111° - 21°) = sin 90° = 1 б) [latex] \frac{cos 23^o*cos 22^o-sin 23^o*sin 22^o}{sin 19^o*cos 26^o+sin 26^o*cos 19^o}=\frac{cos (23^o+ 22^o)}{sin (19^o+26^o)}=\frac{cos 45^o}{sin 45^o}=ctg45^o=1 [/latex] в) [latex]2sin \frac{5 \pi }{12} *cos\frac{5 \pi }{12}=sin\frac{10\pi }{12}=sin\frac{5\pi }{6}=sin( \pi -\frac{\pi }{6})=sin\frac{\pi }{6}=\frac{1}{2}[/latex] г) cos 1990° = cos (5·360° + 190°) = cos 190° = cos (180° + 10°) = - cos 10° ≈ - 0,9848 4) a) [latex]sinx=- \frac{ \sqrt{2} }{2} \\ x=(-1)^{k+1}* \frac{ \pi }{4}+ \pi k, kEZ [/latex] б) [latex]cos 8x = 0 \\ 8x = \frac{ \pi}{2}+ \pi k, kEZ \\x = \frac{ \pi}{16}+ \frac{ \pi k}{8}, kEZ [/latex] в) [latex]2sin \frac{x}{5} =-1 \\ sin \frac{x}{5}=- \frac{1}{2} \\\frac{x}{5}=(-1)^{k+1} \frac{ \pi }{6}+ \pi k,kEZ \\x=(-1)^{k+1} \frac{5 \pi }{6}+ 5\pi k,kEZ [/latex] г) [latex]tg x = 1 \\ x = \frac{ \pi }{4} + \pi k,kEZ[/latex]