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受欢迎的三角函数 >

sin^2(x)+0.49=1

解答

sin^{2} (x) + 0.49 = 1

解答

x = 0.79539 \dots + 2 πn, x = π - 0.79539 \dots + 2 πn, x = - 0.79539 \dots + 2 πn, x = π + 0.79539 \dots + 2 πn

+1

度数

x = 45.57299 \dots^{\circ} + 36 0^{\circ} n, x = 134.42700 \dots^{\circ} + 36 0^{\circ} n, x = - 45.57299 \dots^{\circ} + 36 0^{\circ} n, x = 225.57299 \dots^{\circ} + 36 0^{\circ} n

求解步骤

sin^{2} (x) + 0.49 = 1

用替代法求解

sin^{2} (x) + 0.49 = 1

令

: sin (x) = u

u^{2} + 0.49 = 1

u^{2} + 0.49 = 1 : u = 0.51, u = - 0.51

u^{2} + 0.49 = 1

将

0.49

到右边

u^{2} + 0.49 = 1

两边减去

0.49

u^{2} + 0.49 - 0.49 = 1 - 0.49

化简

u^{2} = 0.51

u^{2} = 0.51

对于

x^{2} = f (a)

解为

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

u = 0.51, u = - 0.51

u = sin (x)

代回

sin (x) = 0.51, sin (x) = - 0.51

sin (x) = 0.51, sin (x) = - 0.51

sin (x) = 0.51 : x = arcsin (0.51) + 2 πn, x = π - arcsin (0.51) + 2 πn

sin (x) = 0.51

使用反三角函数性质

sin (x) = 0.51

sin (x) = 0.51

的通解

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

x = arcsin (0.51) + 2 πn, x = π - arcsin (0.51) + 2 πn

x = arcsin (0.51) + 2 πn, x = π - arcsin (0.51) + 2 πn

sin (x) = - 0.51 : x = arcsin (- 0.51) + 2 πn, x = π + arcsin (0.51) + 2 πn

sin (x) = - 0.51

使用反三角函数性质

sin (x) = - 0.51

sin (x) = - 0.51

的通解

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

x = arcsin (- 0.51) + 2 πn, x = π + arcsin (0.51) + 2 πn

x = arcsin (- 0.51) + 2 πn, x = π + arcsin (0.51) + 2 πn

合并所有解

x = arcsin (0.51) + 2 πn, x = π - arcsin (0.51) + 2 πn, x = arcsin (- 0.51) + 2 πn, x = π + arcsin (0.51) + 2 πn

以小数形式表示解

x = 0.79539 \dots + 2 πn, x = π - 0.79539 \dots + 2 πn, x = - 0.79539 \dots + 2 πn, x = π + 0.79539 \dots + 2 πn

作图

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