Напомним формулы приведения:
Для углов \(\displaystyle 0^{\circ}<\alpha<90^{\circ}{\small:}\)
\(\displaystyle \sin(90^{\circ}-\alpha)=\cos\alpha\) и \(\displaystyle \cos(90^{\circ}-\alpha)=\sin\alpha\small,\)
для углов \(\displaystyle 0^{\circ}<\alpha<180^{\circ}{\small:}\)
\(\displaystyle \sin(180^{\circ}-\alpha)=\sin\alpha\) и \(\displaystyle \cos(180^{\circ}-\alpha)=-\cos\alpha\small.\)
Используя формулы, заполните пропуски в таблице:
| \(\displaystyle 30^{\circ}\) | \(\displaystyle 45^{\circ}\) | \(\displaystyle 60^{\circ}\) | |
| \(\displaystyle \sin\alpha\) | \(\displaystyle \frac{1}{2}\) | \(\displaystyle \frac{\sqrt{3}}{2}\) | |
| \(\displaystyle \cos\alpha\) | \(\displaystyle \frac{\sqrt{2}}{2}\) |
Заполним столбцы таблицы \(\displaystyle 30^{\circ},\,45^{\circ}\) и \(\displaystyle 60^{\circ}\small,\) используя формулы:
Для углов \(\displaystyle 0^{\circ}<\alpha<90^{\circ}{\small:}\)
\(\displaystyle \sin(90^{\circ}-\alpha)=\cos\alpha\) и \(\displaystyle \cos(90^{\circ}-\alpha)=\sin\alpha\small.\)
Воспользуемся формулами:
- \(\displaystyle \cos30^{\circ}=\sin(90^{\circ}-30^{\circ})=\sin60^{\circ}=\frac{\sqrt{3}}{2}\small,\)
- \(\displaystyle \sin45^{\circ}=\cos(90^{\circ}-45^{\circ})=\cos45^{\circ}=\frac{\sqrt{2}}{2}\small,\)
- \(\displaystyle \cos60^{\circ}=\sin(90^{\circ}-60^{\circ})=\sin30^{\circ}=\frac{1}{2}\small.\)
Получаем таблицу:
| \(\displaystyle 30^{\circ}\) | \(\displaystyle 45^{\circ}\) | \(\displaystyle 60^{\circ}\) | |
| \(\displaystyle \sin\alpha\) | \(\displaystyle \frac{1}{2}\) | \(\displaystyle \frac{\sqrt{2}}{2}\) | \(\displaystyle \frac{\sqrt{3}}{2}\) |
| \(\displaystyle \cos\alpha\) | \(\displaystyle \frac{\sqrt{3}}{2}\) | \(\displaystyle \frac{\sqrt{2}}{2}\) | \(\displaystyle \frac{1}{2}\) |