Z własności trygonometrycznych:
[[1]] [tex]tg\alpha=\frac{sin\alpha}{cos\alpha}[/tex]
zatem:
[tex]0,7=\frac{sin\alpha}{cos\alpha} \\\\0,7cos\alpha=sin\alpha[/tex]
[[2]] [tex]sin^2\alpha+cos^2\alpha=1[/tex]
podstawmy sinus:
[tex](\frac{7cos\alpha}{10})^2+cos^2\alpha=1\\\\\frac{49cos^2\alpha}{100}+\frac{100cos^2\alpha}{100}=1\\\\\frac{149}{100}cos^2\alpha=1 |\cdot\frac{100}{149} \\\\cos^2\alpha=\frac{100}{149} \\\\cos\alpha=\sqrt{\frac{100}{149}}=\frac{10}{\sqrt{149} } =\frac{10\sqrt{149} }{149}[/tex]
wg wzoru [[2]] otrzymujemy też:
[tex]sin\alpha=\sqrt{1-cos^2\alpha}[/tex] i podstawiam za [tex]cos^2\alpha[/tex]:
[tex]sin\alpha=\sqrt{1-\frac{100}{149} }=\sqrt{\frac{49}{149} } =\frac{7}{\sqrt{149} } =\frac{7\sqrt{149} }{149}[/tex]