Question

Найдите значение sin α , tgα и сtgα, если cos α =
$\frac{8}{17}$
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Answer 1

Ответ:

$sin^2\alpha + cos^2\alpha =1$

$cos\alpha =\frac{8}{17}$

$sin \alpha =\sqrt{1-cos^{2} \alpha}=\sqrt{ 1-(\frac{8}{17})^2} = \sqrt{1-\frac{64}{289}} =\sqrt{\frac{225}{289}} =\frac{15}{17}$

$tg\alpha =\frac{sin\alpha }{cos\alpha } =\frac{15}{17}:\frac{8}{17}=\frac{15}{17}*\frac{17}{8}= \frac{15}{8}$

$ctg\alpha =\frac{cos\alpha }{sin\alpha } =\frac{8}{17}:\frac{15}{17} =\frac{8}{17} *\frac{17}{15}=\frac{8}{15}$