cos(x)= 5/6

解答

cos (x) = \frac{5}{6}

x = 0.58568 \dots + 2 πn, x = 2 π - 0.58568 \dots + 2 πn

度数

x = 33.55730 \dots^{\circ} + 36 0^{\circ} n, x = 326.44269 \dots^{\circ} + 36 0^{\circ} n

求解步骤

cos (x) = \frac{5}{6}

使用反三角函数性质

cos (x) = \frac{5}{6}

cos (x) = \frac{5}{6}

的通解

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

x = arccos (\frac{5}{6}) + 2 πn, x = 2 π - arccos (\frac{5}{6}) + 2 πn

x = arccos (\frac{5}{6}) + 2 πn, x = 2 π - arccos (\frac{5}{6}) + 2 πn

以小数形式表示解

x = 0.58568 \dots + 2 πn, x = 2 π - 0.58568 \dots + 2 πn

1 - tan^{2} (x) = 0

cos (x) cos (3 x) - sin (x) sin (3 x) = 0

(cot (θ) - 1) (sin (θ) - 1) = 0

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

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