Упр.601 ГДЗ Алимов 10-11 класс (Алгебра)

601 1) cos(arcsin3/5);
2) cos( arcsin(-4/5));
3) cos(arcsin(-1/3));
4) cos(arcsin 1/4).

1. $$\cos\left(\arcsin\frac{3}{5}\right)=\sqrt{1-\sin^2\left(\arcsin\frac{3}{5}\right)}=\sqrt{1-\left(\frac{3}{5}\right)^2}=\sqrt{1-\frac{9}{25}}=\sqrt{\frac{16}{25}}=\frac{4}{5}.$$

2. $$\cos\left(\arcsin\left(-\frac{4}{5}\right)\right)=\sqrt{1-\sin^2\left(\arcsin\left(-\frac{4}{5}\right)\right)}=\sqrt{1-\left(-\frac{4}{5}\right)^2}=\sqrt{1-\frac{16}{25}}=\sqrt{\frac{9}{25}}=\frac{3}{5}.$$

3. $$\cos\left(\arcsin\left(-\frac{1}{3}\right)\right)=\sqrt{1-\sin^2\left(\arcsin\left(-\frac{1}{3}\right)\right)}=\sqrt{1-\left(-\frac{1}{3}\right)^2}=\sqrt{1-\frac{1}{9}}=\sqrt{\frac{8}{9}}=\frac{2\sqrt{2}}{3}.$$

4. $$\cos\left(\arcsin\frac{1}{4}\right)=\sqrt{1-\sin^2\left(\arcsin\frac{1}{4}\right)}=\sqrt{1-\left(\frac{1}{4}\right)^2}=\sqrt{1-\frac{1}{16}}=\sqrt{\frac{15}{16}}=\frac{\sqrt{15}}{4}.$$

Ответ

$$\frac{4}{5};\ \frac{3}{5};\ \frac{2\sqrt{2}}{3};\ \frac{\sqrt{15}}{4}.$$