sin(x)= 10/25

解答

sin (x) = \frac{10}{25}

x = 0.41151 \dots + 2 πn, x = π - 0.41151 \dots + 2 πn

度数

x = 23.57817 \dots^{\circ} + 36 0^{\circ} n, x = 156.42182 \dots^{\circ} + 36 0^{\circ} n

求解步骤

sin (x) = \frac{10}{25}

约分:

5

sin (x) = \frac{2}{5}

使用反三角函数性质

sin (x) = \frac{2}{5}

sin (x) = \frac{2}{5}

的通解

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

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

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

以小数形式表示解

x = 0.41151 \dots + 2 πn, x = π - 0.41151 \dots + 2 πn

\frac{tan ( x )}{sin ( x )} = cos (x)

4 tan^{2} (x) + 7 tan (x) - 4 = 0

tan (θ) = - 1 - 3

so l v e f or y, v = (1 - 4 cos (5 y))^{- \frac{1}{2}}

cos^{2} (β) = \frac{16}{25}, 0 \leq β \leq 2 π