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受欢迎的三角函数 >

sin^2(x)-2/3 =0

解答

sin^{2} (x) - \frac{2}{3} = 0

解答

x = 0.95531 \dots + 2 πn, x = π - 0.95531 \dots + 2 πn, x = - 0.95531 \dots + 2 πn, x = π + 0.95531 \dots + 2 πn

+1

度数

x = 54.73561 \dots^{\circ} + 36 0^{\circ} n, x = 125.26438 \dots^{\circ} + 36 0^{\circ} n, x = - 54.73561 \dots^{\circ} + 36 0^{\circ} n, x = 234.73561 \dots^{\circ} + 36 0^{\circ} n

求解步骤

sin^{2} (x) - \frac{2}{3} = 0

用替代法求解

sin^{2} (x) - \frac{2}{3} = 0

令

: sin (x) = u

u^{2} - \frac{2}{3} = 0

u^{2} - \frac{2}{3} = 0 : u = \frac{2}{3}, u = - \frac{2}{3}

u^{2} - \frac{2}{3} = 0

将

\frac{2}{3}

到右边

u^{2} - \frac{2}{3} = 0

两边加上

\frac{2}{3}

u^{2} - \frac{2}{3} + \frac{2}{3} = 0 + \frac{2}{3}

化简

u^{2} = \frac{2}{3}

u^{2} = \frac{2}{3}

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = \frac{2}{3}, u = - \frac{2}{3}

u = sin (x)

代回

sin (x) = \frac{2}{3}, sin (x) = - \frac{2}{3}

sin (x) = \frac{2}{3}, sin (x) = - \frac{2}{3}

sin (x) = \frac{2}{3} : x = arcsin (\frac{2}{3}) + 2 πn, x = π - arcsin (\frac{2}{3}) + 2 πn

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

使用反三角函数性质

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

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

的通解

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

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

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

sin (x) = - \frac{2}{3} : x = arcsin (- \frac{2}{3}) + 2 πn, x = π + arcsin (\frac{2}{3}) + 2 πn

sin (x) = - \frac{2}{3}

使用反三角函数性质

sin (x) = - \frac{2}{3}

sin (x) = - \frac{2}{3}

的通解

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

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

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

合并所有解

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

以小数形式表示解

x = 0.95531 \dots + 2 πn, x = π - 0.95531 \dots + 2 πn, x = - 0.95531 \dots + 2 πn, x = π + 0.95531 \dots + 2 πn

作图

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