全文
θ x r y
日付( ⽉ ⽇ 曜⽇ )
名前 ( ）
1
＞ 第３章 図形 計量 ＞ 第１節 三⾓⽐ ＞ 第２講：三⾓⽐ 相互関係 数
例題
のとき，次の値を求めなさい。ただし，
は鋭⾓とする。
１
２
３
(1)
解
(1) (2)
cosθ = 5 9 cos2θ + sin2θ = 1から，
cos2θ = 1−sin2θ
= 1− (2 3)
2
= 59
であるから，
cosθ > 0
= 5 3
tanθ = sinθ cosθ
= 25
23 5
3 = 23 ÷ 35
= 23 × 3 5
= 2 5 5 ２
sinθ = y
r ⇒ y = rsinθ cosθ = x
r ⇒ x = rcosθ
三平⽅の定理より，
x2+y2= r2
(rcosθ)2+ (rsinθ)2 = r2 r2(cosθ)2+r2(sinθ)2 = r2
cos2θ + sin2θ = 1
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