Question

найти косинус альфа и тангенс если синус 1/2​

Answer 1

Ответ:

$cos \alpha = \frac{\sqrt{3}}{2}\\\\tg\alpha = \frac{1}{\sqrt{3}}$

Объяснение:

1.

$sin^{2}\alpha + cos^{2} \alpha = 1\\\\cos^{2} \alpha = 1 - sin^{2}\alpha\\\\cos \alpha = \sqrt{1 - sin^{2}\alpha}\\\\cos \alpha = \sqrt{1 - (\frac{1}{2} )^{2} }\\\\cos \alpha = \sqrt{1 - \frac{1}{4}}\\\\cos \alpha = \sqrt{ \frac{4-1}{4}}\\\\cos \alpha = \sqrt{ \frac{3}{4}}\\\\cos \alpha = \frac{\sqrt{3}}{\sqrt{4}}\\\\cos \alpha = \frac{\sqrt{3}}{2}$

2.

$tg\alpha = \frac{sin\alpha }{cos\alpha } \\\\tg\alpha = \frac{1}{2}:\frac{\sqrt{3}}{2}\\\\tg\alpha = \frac{1}{2}*\frac{2}{\sqrt{3}}\\\\tg\alpha = \frac{1}{1}*\frac{1}{\sqrt{3}}\\\\tg\alpha = \frac{1}{\sqrt{3}}$