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受欢迎的三角函数 >

sin^{22}(x)= 1/4

解答

sin^{22} (x) = \frac{1}{4}

解答

x = 1.21951 \dots + 2 πn, x = π - 1.21951 \dots + 2 πn, x = - 1.21951 \dots + 2 πn, x = π + 1.21951 \dots + 2 πn

+1

度数

x = 69.87278 \dots^{\circ} + 36 0^{\circ} n, x = 110.12721 \dots^{\circ} + 36 0^{\circ} n, x = - 69.87278 \dots^{\circ} + 36 0^{\circ} n, x = 249.87278 \dots^{\circ} + 36 0^{\circ} n

求解步骤

sin^{22} (x) = \frac{1}{4}

用替代法求解

sin^{22} (x) = \frac{1}{4}

令

: sin (x) = u

u^{22} = \frac{1}{4}

u^{22} = \frac{1}{4} : u = 22 \frac{1}{4}, u = - 22 \frac{1}{4}

u^{22} = \frac{1}{4}

对于

x^{n} = f (a)

，n 为偶数，解为

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

u = 22 \frac{1}{4}, u = - 22 \frac{1}{4}

u = sin (x)

代回

sin (x) = 22 \frac{1}{4}, sin (x) = - 22 \frac{1}{4}

sin (x) = 22 \frac{1}{4}, sin (x) = - 22 \frac{1}{4}

sin (x) = 22 \frac{1}{4} : x = arcsin (22 \frac{1}{4}) + 2 πn, x = π - arcsin (22 \frac{1}{4}) + 2 πn

sin (x) = 22 \frac{1}{4}

使用反三角函数性质

sin (x) = 22 \frac{1}{4}

sin (x) = 22 \frac{1}{4}

的通解

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

x = arcsin (22 \frac{1}{4}) + 2 πn, x = π - arcsin (22 \frac{1}{4}) + 2 πn

x = arcsin (22 \frac{1}{4}) + 2 πn, x = π - arcsin (22 \frac{1}{4}) + 2 πn

sin (x) = - 22 \frac{1}{4} : x = arcsin (- 22 \frac{1}{4}) + 2 πn, x = π + arcsin (22 \frac{1}{4}) + 2 πn

sin (x) = - 22 \frac{1}{4}

使用反三角函数性质

sin (x) = - 22 \frac{1}{4}

sin (x) = - 22 \frac{1}{4}

的通解

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

x = arcsin (- 22 \frac{1}{4}) + 2 πn, x = π + arcsin (22 \frac{1}{4}) + 2 πn

x = arcsin (- 22 \frac{1}{4}) + 2 πn, x = π + arcsin (22 \frac{1}{4}) + 2 πn

合并所有解

x = arcsin (22 \frac{1}{4}) + 2 πn, x = π - arcsin (22 \frac{1}{4}) + 2 πn, x = arcsin (- 22 \frac{1}{4}) + 2 πn, x = π + arcsin (22 \frac{1}{4}) + 2 πn

以小数形式表示解

x = 1.21951 \dots + 2 πn, x = π - 1.21951 \dots + 2 πn, x = - 1.21951 \dots + 2 πn, x = π + 1.21951 \dots + 2 πn

作图

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