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受欢迎的三角函数 >

6sin^2(x)=5

解答

6 sin^{2} (x) = 5

解答

x = 1.15026 \dots + 2 πn, x = π - 1.15026 \dots + 2 πn, x = - 1.15026 \dots + 2 πn, x = π + 1.15026 \dots + 2 πn

+1

度数

x = 65.90515 \dots^{\circ} + 36 0^{\circ} n, x = 114.09484 \dots^{\circ} + 36 0^{\circ} n, x = - 65.90515 \dots^{\circ} + 36 0^{\circ} n, x = 245.90515 \dots^{\circ} + 36 0^{\circ} n

求解步骤

6 sin^{2} (x) = 5

用替代法求解

6 sin^{2} (x) = 5

令

: sin (x) = u

6 u^{2} = 5

6 u^{2} = 5 : u = \frac{5}{6}, u = - \frac{5}{6}

6 u^{2} = 5

两边除以

6

6 u^{2} = 5

两边除以

6

\frac{6 u ^{2}}{6} = \frac{5}{6}

化简

u^{2} = \frac{5}{6}

u^{2} = \frac{5}{6}

对于

x^{2} = f (a)

解为

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

u = \frac{5}{6}, u = - \frac{5}{6}

u = sin (x)

代回

sin (x) = \frac{5}{6}, sin (x) = - \frac{5}{6}

sin (x) = \frac{5}{6}, sin (x) = - \frac{5}{6}

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

sin (x) = \frac{5}{6}

使用反三角函数性质

sin (x) = \frac{5}{6}

sin (x) = \frac{5}{6}

的通解

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

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

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

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

sin (x) = - \frac{5}{6}

使用反三角函数性质

sin (x) = - \frac{5}{6}

sin (x) = - \frac{5}{6}

的通解

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

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

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

合并所有解

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

以小数形式表示解

x = 1.15026 \dots + 2 πn, x = π - 1.15026 \dots + 2 πn, x = - 1.15026 \dots + 2 πn, x = π + 1.15026 \dots + 2 πn

作图

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