【高校数学Ⅰ】3-2-1 鈍角の三角比｜問題集
1.次の値を求めなさい。
(1)\(\sin135^{\circ}\)
\(\displaystyle \frac{1}{\sqrt{2}}\)
(2)\(\cos150^{\circ}\)
\(\displaystyle -\frac{\sqrt{3}}{2}\)
(3)\(\tan120^{\circ}\)
\(-\sqrt{3}\)
(4)\(\sin90^{\circ}\)
\(1\)
(5)\(\sin0^{\circ}\)
\(0\)
(6)\(\cos90^{\circ}\)
\(0\)
(7)\(\cos180^{\circ}\)
\(-1\)
(8)\(\sin120^{\circ}\)
\(\displaystyle \frac{\sqrt{3}}{2}\)
(9)\(\cos135^{\circ}\)
\(\displaystyle -\frac{1}{\sqrt{2}}\)
(10)\(\tan150^{\circ}\)
\(\displaystyle -\frac{1}{\sqrt{3}}\)
2.次の三角比を\(90^{\circ}\)以下の角の三角比で表しなさい。
(1)\(\sin140^{\circ}\)
\(\sin40^{\circ}\)
(2)\(\cos165^{\circ}\)
\(-\cos15^{\circ}\)
(3)\(\tan130^{\circ}\)
\(-\tan50^{\circ}\)
(4)\(\sin160^{\circ}\)
\(\sin20^{\circ}\)
(5)\(\cos105^{\circ}\)
\(-\cos75^{\circ}\)
(6)\(\tan128^{\circ}\)
\(-\tan52^{\circ}\)
3.次の式の値を求めなさい。
(1)\(\sin70^{\circ}+\cos100^{\circ}+\sin170^{\circ}+\cos160^{\circ}\)
\(=\cos20^{\circ}-\cos80^{\circ}+\sin10^{\circ}-\cos20^{\circ}\)
\(=\cos20^{\circ}-\sin10^{\circ}+\sin10^{\circ}-\cos20^{\circ}\)
\(=0\)
\(=\cos20^{\circ}-\sin10^{\circ}+\sin10^{\circ}-\cos20^{\circ}\)
\(=0\)
(2)\(\sin140^{\circ}\cos50^{\circ}+\cos40^{\circ}\sin50^{\circ}\)
\(=\sin40^{\circ}\sin40^{\circ}+\cos40^{\circ}\cos40^{\circ}\)
\(=\sin^2 40^{\circ}+\cos^2 40^{\circ}\)
\(=1\)
\(=\sin^2 40^{\circ}+\cos^2 40^{\circ}\)
\(=1\)
次の学習に進もう！