sin(x)= 19/50

解答

sin (x) = \frac{19}{50}

x = 0.38979 \dots + 2 πn, x = π - 0.38979 \dots + 2 πn

度数

x = 22.33368 \dots^{\circ} + 36 0^{\circ} n, x = 157.66631 \dots^{\circ} + 36 0^{\circ} n

求解步骤

sin (x) = \frac{19}{50}

使用反三角函数性质

sin (x) = \frac{19}{50}

sin (x) = \frac{19}{50}

的通解

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

x = arcsin (\frac{19}{50}) + 2 πn, x = π - arcsin (\frac{19}{50}) + 2 πn

x = arcsin (\frac{19}{50}) + 2 πn, x = π - arcsin (\frac{19}{50}) + 2 πn

以小数形式表示解

x = 0.38979 \dots + 2 πn, x = π - 0.38979 \dots + 2 πn

5 sin (2 x - \frac{π}{2}) = 0.5

5 sin (x) = 3 sin (x) + cos (x)

3 - 3 cos (5 x) = 3 cos (5 x)

\frac{1}{1 - cos ( x )} + \frac{1}{1 + cos ( x )} = 2 sec^{2} (x)

2 cos^{2} (θ) - sin (θ) = 2