cos(a)= 5/8

解答

cos (a) = \frac{5}{8}

a = 0.89566 \dots + 2 πn, a = 2 π - 0.89566 \dots + 2 πn

度数

a = 51.31781 \dots^{\circ} + 36 0^{\circ} n, a = 308.68218 \dots^{\circ} + 36 0^{\circ} n

求解步骤

cos (a) = \frac{5}{8}

使用反三角函数性质

cos (a) = \frac{5}{8}

cos (a) = \frac{5}{8}

的通解

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

a = arccos (\frac{5}{8}) + 2 πn, a = 2 π - arccos (\frac{5}{8}) + 2 πn

a = arccos (\frac{5}{8}) + 2 πn, a = 2 π - arccos (\frac{5}{8}) + 2 πn

以小数形式表示解

a = 0.89566 \dots + 2 πn, a = 2 π - 0.89566 \dots + 2 πn

tan (θ) sin^{2} (θ) = tan (θ)

cos (θ) = \frac{5}{8}

cot (θ) + 3 = 0, 0 \leq θ \leq 2 π

2 cos (θ) - 2 = 0, 0 \leq θ \leq 2 π

4 sin^{2} (x) - 7 cos (x) = 2