第8章周期関数Periodic Functions

We know the tangent function can be used to find distances, such as the height of a building, mountain, or flagpole. But what if we want to measure repeated occurrences of distance? Imagine, for example, a fire truck parked next to a warehouse. The rotating light from the truck would travel across the wall of the warehouse in regular intervals. If the input is time, the output would be the distance the beam of light travels. The beam of light would repeat the distance at regular intervals. The tangent function can be used to approximate this distance. Asymptotes would be needed to illustrate the repeated cycles when the beam runs parallel to the wall because, seemingly, the beam of light could appear to extend forever. The graph of the tangent function would clearly illustrate the repeated intervals. In this section, we will explore the graphs of the tangent and other trigonometric functions.

正接関数を使えば、建物・山・旗竿の高さのような距離が求められると分かっている。だが、繰り返し現れる距離を測りたいならどうか。たとえば、倉庫の隣に停まった消防車を思い浮かべよう。この車の回転灯は、決まった間隔で倉庫の壁を横切る。入力が時間なら、出力は光の筋が進む距離になる。光の筋は決まった間隔でその距離を繰り返す。正接関数を使えば、この距離を近似できる。光の筋が壁と平行になるとき、光は見かけ上どこまでも伸びうるので、繰り返す周期を示すには漸近線が要る。正接関数のグラフは、この繰り返す間隔をはっきり示す。この節では、正接関数とそのほかの三角関数のグラフを調べる。