sin(b)= 2/3

解答

sin (b) = \frac{2}{3}

b = 0.72972 \dots + 2 πn, b = π - 0.72972 \dots + 2 πn

度数

b = 41.81031 \dots^{\circ} + 36 0^{\circ} n, b = 138.18968 \dots^{\circ} + 36 0^{\circ} n

求解步骤

sin (b) = \frac{2}{3}

使用反三角函数性质

sin (b) = \frac{2}{3}

sin (b) = \frac{2}{3}

的通解

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

b = arcsin (\frac{2}{3}) + 2 πn, b = π - arcsin (\frac{2}{3}) + 2 πn

b = arcsin (\frac{2}{3}) + 2 πn, b = π - arcsin (\frac{2}{3}) + 2 πn

以小数形式表示解

b = 0.72972 \dots + 2 πn, b = π - 0.72972 \dots + 2 πn

(- 5 cos (x) - 6 sin (x))^{2} - 11 sin^{2} (x) = 25

2 sin^{2} (x) - 9 sin (x) - 5 = 0

2 sin^{2} (x) = 5 cos (x) - 1

so l v e f or x, sec (x + 1 0^{\circ}) = 5.759

tan (x) cot (x) + 2 cot (x) = 0