Question

Знайдіть tga якщо sina=4÷5​

Answer 1

Tga=?;sina=4/5


cosa=±√(1-sin²a)=±√(1-16/25)=±√9/25=±3/5

tga=sina/cosa=(4/5):3/5=4/3
tga=-4/3

otvet ±4/3

Answer 2

1. Если угол α<90°:

$\displaystyle tg\alpha=\frac{\sin\alpha}{\cos\alpha} =\frac{\sin\alpha}{\sqrt{1-\sin^2\alpha} } =\frac{4}{5\sqrt{1-\frac{16}{25} } } =\frac{4}{5\sqrt{\frac{9}{25} } }=\frac{4}{5\cdot\frac{3}{5} } = \frac{4\cdot5}{3\cdot5} =\frac{4}{3}$

2. Если угол α>90°:

$\displaystyle tg\alpha=\frac{\sin\alpha}{\cos\alpha}=\frac{\sin(180^\circ-\alpha)}{\cos(180^\circ-\alpha)}=\frac{\sin\alpha}{-\cos\alpha}=\frac{\sin\alpha}{-\sqrt{1-\sin^2\alpha}}=-\frac{4}{5\cdot\sqrt{1-\frac{16}{25}}} =-\frac{4}{5\cdot\sqrt{\frac{9}{25}}}=-\frac{4}{5\cdot\frac{3}{5}} =-\frac{4\cdot5}{3\cdot5}=-\frac{4}{3}$