zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

sin^2(x)=0.85

解答

sin^{2} (x) = 0.85

解答

x = 1.17309 \dots + 2 πn, x = π - 1.17309 \dots + 2 πn, x = - 1.17309 \dots + 2 πn, x = π + 1.17309 \dots + 2 πn

+1

度数

x = 67.21350 \dots^{\circ} + 36 0^{\circ} n, x = 112.78649 \dots^{\circ} + 36 0^{\circ} n, x = - 67.21350 \dots^{\circ} + 36 0^{\circ} n, x = 247.21350 \dots^{\circ} + 36 0^{\circ} n

求解步骤

sin^{2} (x) = 0.85

用替代法求解

sin^{2} (x) = 0.85

令

: sin (x) = u

u^{2} = 0.85

u^{2} = 0.85 : u = 0.85, u = - 0.85

u^{2} = 0.85

对于

x^{2} = f (a)

解为

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

u = 0.85, u = - 0.85

u = sin (x)

代回

sin (x) = 0.85, sin (x) = - 0.85

sin (x) = 0.85, sin (x) = - 0.85

sin (x) = 0.85 : x = arcsin (0.85) + 2 πn, x = π - arcsin (0.85) + 2 πn

sin (x) = 0.85

使用反三角函数性质

sin (x) = 0.85

sin (x) = 0.85

的通解

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

x = arcsin (0.85) + 2 πn, x = π - arcsin (0.85) + 2 πn

x = arcsin (0.85) + 2 πn, x = π - arcsin (0.85) + 2 πn

sin (x) = - 0.85 : x = arcsin (- 0.85) + 2 πn, x = π + arcsin (0.85) + 2 πn

sin (x) = - 0.85

使用反三角函数性质

sin (x) = - 0.85

sin (x) = - 0.85

的通解

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

x = arcsin (- 0.85) + 2 πn, x = π + arcsin (0.85) + 2 πn

x = arcsin (- 0.85) + 2 πn, x = π + arcsin (0.85) + 2 πn

合并所有解

x = arcsin (0.85) + 2 πn, x = π - arcsin (0.85) + 2 πn, x = arcsin (- 0.85) + 2 πn, x = π + arcsin (0.85) + 2 πn

以小数形式表示解

x = 1.17309 \dots + 2 πn, x = π - 1.17309 \dots + 2 πn, x = - 1.17309 \dots + 2 πn, x = π + 1.17309 \dots + 2 πn

作图

流行的例子

cos(x-60)=(sqrt(3))/2

cos (x - 6 0^{\circ}) = \frac{3}{2}

(0.5*9.8*l(1-cos(θ)))=0.018

(0.5 \cdot 9.8 \cdot l (1 - cos (θ))) = 0.018

solvefor x,0=-sin(2x)-2cos(x)

so l v e f or x, 0 = - sin (2 x) - 2 cos (x)

sec(θ)=(sqrt(5))/2

sec (θ) = \frac{5}{2}

4 cos (x - 1) = 0