数学B¶
ベクトル¶
1. 円の方程式¶
\[
x^{2} + y^{2} = r^{2}
\]
2. 三角関数¶
2.1. 加法定理¶
2.1.1. 正弦(sin)・余弦(cos)の加法定理¶
\[
\sin(\alpha + \beta) = \sin{\alpha} \cdot \cos{\beta} + \cos{\alpha} \cdot \sin{\beta}
\]
\[
\sin(\alpha + \beta) = \sin{\alpha} \cdot \cos{\beta} - \cos{\alpha} \cdot \sin{\beta}
\]
\[
\cos(\alpha + \beta) = \cos{\alpha} \cdot \cos{\beta} - \sin{\alpha} \cdot \sin{\beta}
\]
\[
\cos(\alpha - \beta) = \cos{\alpha} \cdot \cos{\beta} + \sin{\alpha} \cdot \sin{\beta}
\]
2.1.2. 正接(tan)の加法定理¶
\[
\tan(\alpha + \beta) = \frac{\tan{\alpha} + \tan{\beta}}{1 - \tan{\alpha} \cdot \tan{\beta} }
\]
\[
\tan(\alpha - \beta) = \frac{\tan{\alpha} - \tan{\beta}}{1 + \tan{\alpha} \cdot \tan{\beta} }
\]
2.2. 倍角・半角¶
2.2.1. ２倍角の公式¶
\[
\sin{2\alpha} = 2 \cdot \sin{\alpha} \cdot \cos{\alpha}
\]
\[
\sin(\alpha + \alpha) = \sin{\alpha} \cdot \cos{\alpha} + \cos{\alpha} \cdot \sin{\alpha}
\]
\[
\cos{2\alpha} = \cos^2{\alpha} - \sin^2{\alpha}
\]
\[
\cos(\alpha + \alpha) = \cos{\alpha} \cdot \cos{\alpha} - \sin{\alpha} \cdot \sin{\alpha}
\]