sin(θ)= 5/6

解答

sin (θ) = \frac{5}{6}

θ = 0.98511 \dots + 2 πn, θ = π - 0.98511 \dots + 2 πn

度数

θ = 56.44269 \dots^{\circ} + 36 0^{\circ} n, θ = 123.55730 \dots^{\circ} + 36 0^{\circ} n

求解步骤

sin (θ) = \frac{5}{6}

使用反三角函数性质

sin (θ) = \frac{5}{6}

sin (θ) = \frac{5}{6}

的通解

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

θ = arcsin (\frac{5}{6}) + 2 πn, θ = π - arcsin (\frac{5}{6}) + 2 πn

θ = arcsin (\frac{5}{6}) + 2 πn, θ = π - arcsin (\frac{5}{6}) + 2 πn

以小数形式表示解

θ = 0.98511 \dots + 2 πn, θ = π - 0.98511 \dots + 2 πn

3 tan^{2} (x) = 3 tan (x)

2 sec (x) - 4 cos (x) = 0

cos (x + 1) = sin (x)

2 sin^{2} (θ) = 2 + cos (2 θ)

tan^{2} (x) - 1 = 0, 0 \leq x \leq 2 π