cos(x)= 8/15

解答

cos (x) = \frac{8}{15}

x = 1.00826 \dots + 2 πn, x = 2 π - 1.00826 \dots + 2 πn

度数

x = 57.76904 \dots^{\circ} + 36 0^{\circ} n, x = 302.23095 \dots^{\circ} + 36 0^{\circ} n

求解步骤

cos (x) = \frac{8}{15}

使用反三角函数性质

cos (x) = \frac{8}{15}

cos (x) = \frac{8}{15}

的通解

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

x = arccos (\frac{8}{15}) + 2 πn, x = 2 π - arccos (\frac{8}{15}) + 2 πn

x = arccos (\frac{8}{15}) + 2 πn, x = 2 π - arccos (\frac{8}{15}) + 2 πn

以小数形式表示解

x = 1.00826 \dots + 2 πn, x = 2 π - 1.00826 \dots + 2 πn

sin (4 k - 22) = cos (6 k - 13)

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

2 tan (x) sin (x) = 3 tan (x)

tan (x) = - 2 + 1

cos (x) = 0.914