cos(x)= 5/7

解答

cos (x) = \frac{5}{7}

x = 0.77519 \dots + 2 πn, x = 2 π - 0.77519 \dots + 2 πn

度数

x = 44.41530 \dots^{\circ} + 36 0^{\circ} n, x = 315.58469 \dots^{\circ} + 36 0^{\circ} n

求解步骤

cos (x) = \frac{5}{7}

使用反三角函数性质

cos (x) = \frac{5}{7}

cos (x) = \frac{5}{7}

的通解

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

x = arccos (\frac{5}{7}) + 2 πn, x = 2 π - arccos (\frac{5}{7}) + 2 πn

x = arccos (\frac{5}{7}) + 2 πn, x = 2 π - arccos (\frac{5}{7}) + 2 πn

以小数形式表示解

x = 0.77519 \dots + 2 πn, x = 2 π - 0.77519 \dots + 2 πn

cos (8 x) = 0

sin (x) + 2 sin (x) cos (x) = 0, 0 \leq x \leq 2 π

9 cos^{2} (θ) - 24 sin (θ) - 10 = - 8 sin (θ) + 6

cos^{2} (θ) = sin^{2} (θ) - 1

2 cos (2 θ) = - 3