cos(x)= 2/5

解答

cos (x) = \frac{2}{5}

x = 1.15927 \dots + 2 πn, x = 2 π - 1.15927 \dots + 2 πn

度数

x = 66.42182 \dots^{\circ} + 36 0^{\circ} n, x = 293.57817 \dots^{\circ} + 36 0^{\circ} n

求解步骤

cos (x) = \frac{2}{5}

使用反三角函数性质

cos (x) = \frac{2}{5}

cos (x) = \frac{2}{5}

的通解

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

x = arccos (\frac{2}{5}) + 2 πn, x = 2 π - arccos (\frac{2}{5}) + 2 πn

x = arccos (\frac{2}{5}) + 2 πn, x = 2 π - arccos (\frac{2}{5}) + 2 πn

以小数形式表示解

x = 1.15927 \dots + 2 πn, x = 2 π - 1.15927 \dots + 2 πn

sin (θ) + cos (θ) = 2

sin^{2} (x) - cos^{2} (x) = \frac{1}{2}

2 sin^{2} (x) + cos (x) = 0

sec (3 x) = \frac{2}{3}, 0 \leq x \leq 2 π

sec (4 x) - 2 = 0