Question

cos alpha =0.8
alpha є 1чверть
sin 2 alpha = ?

Answer 1

$\displaystyle\\0 < \alpha < \frac{\pi }{2} \ \ \ \Rightarrow \ \ \ Sin\alpha > 0\\\\Cos\alpha =0,8\\\\Sin\alpha =\sqrt{1-Cos^{2} \alpha } =\sqrt{1-(0,8)^{2} } =\sqrt{1-0,64}=\sqrt{0,36} =0,6\\\\\\Sin2\alpha =2\cdot Sin\alpha \cdot Cos\alpha=2\cdot 0,6\cdot 0,8=0,96\\\\\\Otvet \ : \ Sin2\alpha =0,96$

Answer 2

Ответ:

$sin2\alpha=0,96$

Объяснение:

$sin^2\alpha+cos^2\alpha=1\\\\sin^2\alpha+0,8^2=1\\\\sin^2\alpha+0,64=1\\\\sin^2\alpha=1-0,64\\\\sin^2\alpha=0,36\\(a\pha \in (0^o;90^o))\\\\sin\alpha=\sqrt{0,36}\\\\sin\alpha=0,6$

$sin2\alpha=2sin\alpha cos\alpha\\\\sin2\alpha=2\cdot0,8\cdot0,6\\\\sin2\alpha=0,96$