sin(θ)=-8/9

解答

sin (θ) = - \frac{8}{9}

θ = - 1.09491 \dots + 2 πn, θ = π + 1.09491 \dots + 2 πn

度数

θ = - 62.73395 \dots^{\circ} + 36 0^{\circ} n, θ = 242.73395 \dots^{\circ} + 36 0^{\circ} n

求解步骤

sin (θ) = - \frac{8}{9}

使用反三角函数性质

sin (θ) = - \frac{8}{9}

sin (θ) = - \frac{8}{9}

的通解

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

θ = arcsin (- \frac{8}{9}) + 2 πn, θ = π + arcsin (\frac{8}{9}) + 2 πn

θ = arcsin (- \frac{8}{9}) + 2 πn, θ = π + arcsin (\frac{8}{9}) + 2 πn

以小数形式表示解

θ = - 1.09491 \dots + 2 πn, θ = π + 1.09491 \dots + 2 πn

2 sin^{2} (x) + 5 sin (x) - 12 = 0

3 tan (x - \frac{π}{5}) - 1 = 0

so l v e f or x, 0 = 4 - \frac{1}{cos ^{2} ( x )}

tan (θ) = \frac{17}{12}

csc^{2} (θ) = 2 cot (θ)