Question

1)найти и , если и 2) найти и , если и

Answer 1

$1)\; \; cos \alpha =-\frac{2}{5}\; ,\\\\sin \alpha =\pm \sqrt{1-cos^2 \alpha }\; ,\; tg \alpha =\pm \sqrt{\frac{1}{cos^2 \alpha }-1}\\\\\; \; \ \alpha \in (\pi ;\frac{3\pi}{2})\; \; \to \; \; sin \alpha \ \textless \ 0,\; \; tg \alpha \ \textgreater \ 0\\\\sin \alpha =-\sqrt{1-\frac{4}{25}}=-\sqrt{\frac{21}{25}}=-\frac{\sqrt{21}}{5}\\\\tg \alpha =+\sqrt{\frac{25}{4}-1}=\frac{\sqrt{21}}{2}$

$2)\; \; sin \alpha =\frac{3}{4}\\\\ \alpha \in (\frac{\pi}{2};\pi )\; \; \to \; \; cos \alpha \ \textless \ 0\; ,\; \; ctg \alpha \ \textless \ 0\\\\cos \alpha =-\sqrt{1-sin^2 \alpha }=-\sqrt{1-\frac{9}{16}}=-\frac{\sqrt7}{4}\\\\ctg \alpha =-\sqrt{\frac{1}{sin^2 \alpha }-1}=-\sqrt{\frac{16}{9}-1}=-\frac{\sqrt7}{3}$