[tex]\alpha[/tex] - kąt rozwarty
c)
[tex]\sin\alpha=\frac{24}{25}\\\sin^2\alpha+\cos^2\alpha=1\\(\frac{24}{25})^2+cos^2\alpha=1\\\frac{576}{625}+cos^2\alpha=1\\cos^2\alpha=1-\frac{576}{625}\\cos^2\alpha=\frac{49}{625}\\\cos\alpha=\frac{7}{25}\vee\cos\alpha=-\frac{7}{25}[/tex]
ale [tex]\alpha[/tex] - kąt rozwarty, więc
[tex]\cos\alpha=-\frac{7}{25}\\\text{tg}\ \alpha=\frac{\sin\alpha}{\cos\alpha}=\frac{\frac{24}{25}}{-\frac{7}{25}}=\frac{24}{25}*(-\frac{25}{7})=-\frac{24}{7}\\\text{ctg}\ \alpha=\frac{1}{\text{tg}\ \alpha}=-\frac{7}{24}[/tex]
d)
[tex]\text{tg}\ \alpha=-2\\\text{ctg}\ \alpha=\frac{1}{\text{tg}\ \alpha}=-\frac{1}{2}\\\text{tg}\ \alpha=\frac{\sin\alpha}{\cos\alpha}\\\frac{\sin\alpha}{\cos\alpha}=-2\ |*\cos\alpha\\\sin\alpha=-2\cos\alpha\\\sin^2\alpha+\cos^2\alpha=1\\(-2\cos\alpha)^2+\cos^2\alpha=1\\4\cos^2\alpha+\cos^2\alpha=1\\5\cos^2\alpha=1\ |:5\\\cos^2\alpha=\frac{1}{5}\\\cos\alpha=\frac{1}{\sqrt5}=\frac{\sqrt5}{5}\vee \cos\alpha=-\frac{1}{\sqrt5}=-\frac{\sqrt5}{5}[/tex]
ale [tex]\alpha[/tex] - kąt rozwarty, więc
[tex]\cos\alpha=-\frac{\sqrt5}{5}\\\sin\alpha=-2*(-\frac{\sqrt5}{5})=\frac{2\sqrt5}{5}[/tex]
