Question

знайдіть cosa, tga
якщо sinA = -0,8 π<a<3π/2 ​

Answer 1

$\sin\alpha=-0,8~~,~~\pi < \alpha < \dfrac{3\pi}2\\\\\\\cos^2\alpha+\sin^2\alpha=1~~\Rightarrow~~\cos^2\alpha=1-\sin^2\alpha=1-(-0,8)^2=1-0,64=0,36\\\\\\\cos\alpha=\pm\sqrt{0,36}=\pm0,6~~,~~\pi < \alpha < \dfrac{3\pi}2~~\Rightarrow~~\boxed{\cos\alpha=-0,6}\\\\\\\tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}=\dfrac{-0,8}{-0,6}~~\Rightarrow~~\boxed{\tan\alpha=\dfrac{4}{3}}$