Question

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Answer 1

Ответ:

$\displaystyle sint=\frac{7}{25}\\\\cos^2t=1-sin^2t\ \ \Rightarrow \ \ \ cost=\pm \sqrt{1-sin^2t}\\\\\frac{\pi}{2}<t<\pi \ \ \Rightarrow \ \ \ cost<0\ \ ,\ \ cost=-\sqrt{1-sin^2t}\ ,\\\\cost=-\sqrt{1-\frac{49}{625}}=-\sqrt{\frac{576}{625}}=-\frac{24}{25}\\\\\\tgt=\frac{sint}{cost}=\frac{\frac{7}{25}}{-\frac{24}{25}}=-\frac{7}{24}\\\\\\ctgt=\frac{1}{tgt}=-\frac{24}{7}$

Answer 2

α - угол второй четверти , значит : Cosα < 0 , tgα <0 , Ctgα < 0 .

$\displaystyle\bf\\Sin\alpha =\frac{7}{25} \\\\\\Cos\alpha =-\sqrt{1-Sin^{2} \alpha } =-\sqrt{1-\Big(\frac{7}{25} \Big)^{2} } =-\sqrt{1-\frac{49}{625} } =\\\\\\=-\sqrt{\frac{576}{625} } =-\frac{24}{25} \\\\\\tg\alpha =\frac{Sin\alpha }{Cos\alpha } =\frac{7}{25} :\Big(-\frac{24}{25} \Big)=-\frac{7}{25} \cdot\frac{25}{24} =-\frac{7}{24} \\\\\\Ctg\alpha =\frac{1}{tg\alpha } =1:\Big(-\frac{7}{24} \Big)=1\cdot\Big(-\frac{24}{7} \Big)=-3\frac{3}{7}$