こんにちは。相城です。今回は三角比について書いておきます。
,
,
も円で考えれば, 間違いが減るのではないでしょうか。もちろん, 基本的な考え方は, 45
, 45
, 90
や30
, 60
, 90
の直角三角形をイメージして考えるのですが。
円を使ってsin,cos,tan
以下のような半径の円があって, その円周上の点をP(
,
)とする。
とするとき,
,
,
は以下の式で求められます。
定義
ただし,
![Rendered by QuickLaTeX.com \theta=90^{\circ}, 270^{\circ}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-7cd0814b34d28d297ab6b13e98e20dfa_l3.png)
![Rendered by QuickLaTeX.com y](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-5d76ceac31cb52dd9eb4431a14c502dc_l3.png)
![Rendered by QuickLaTeX.com \tan\theta](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-62453fc692083d6721c3ec75c21cf979_l3.png)
図の
![Rendered by QuickLaTeX.com \theta](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-df36b52cea0081617d2fc178107fe54d_l3.png)
![Rendered by QuickLaTeX.com \theta](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-df36b52cea0081617d2fc178107fe54d_l3.png)
![Rendered by QuickLaTeX.com ^{\circ}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-24b5359298fa467a4b68ffc5605538fe_l3.png)
円を使って求めてみよう
せっかくなので, 少し例題をやってきまでょう。
次の値を求めなさい。,
,
![Rendered by QuickLaTeX.com \sin45^{\circ}=\dfrac{y}{r}=\dfrac{1}{\sqrt2}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-a4ed3230ddca634db83cc86259137761_l3.png)
![Rendered by QuickLaTeX.com \cos45^{\circ}=\dfrac{x}{r}=\dfrac{1}{\sqrt2}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-e175991f5a2184e19246aace15382568_l3.png)
![Rendered by QuickLaTeX.com \tan45^{\circ}=\dfrac{y}{x}=\dfrac{1}{1}=1](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-01bcdaf19026eda267b9171c478c9a18_l3.png)
次の値を求めなさい。,
,
![Rendered by QuickLaTeX.com \sin30^{\circ}=\dfrac{y}{r}=\dfrac{1}{2}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-9b63e66608e0779e5e6ca7e21dd70163_l3.png)
![Rendered by QuickLaTeX.com \cos30^{\circ}=\dfrac{x}{r}=\dfrac{\sqrt3}{2}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-a62946ed84e9b435e5ee91ec03f6adfd_l3.png)
![Rendered by QuickLaTeX.com \tan30^{\circ}=\dfrac{y}{x}=\dfrac{1}{\sqrt3}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-d5dd4a5da1cb06a566adde1d04c2bebf_l3.png)
次の値を求めなさい。,
,
![Rendered by QuickLaTeX.com \sin120^{\circ}=\dfrac{y}{r}=\dfrac{\sqrt{3}}{2}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-f7090f552b39d89579272874f2e56f43_l3.png)
![Rendered by QuickLaTeX.com \cos120^{\circ}=\dfrac{x}{r}=\dfrac{-1}{2}=-\dfrac{1}{2}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-2a23eb234346593fa1f6599ecfc89557_l3.png)
![Rendered by QuickLaTeX.com \tan120^{\circ}=\dfrac{y}{x}=\dfrac{\sqrt{3}}{-1}=-\sqrt{3}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-15dc68645e43301bdb8e2c14c2e704ca_l3.png)