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)=0.2

解答

sin^{2} (x) = 0.2

解答

x = 0.46364 \dots + 2 πn, x = π - 0.46364 \dots + 2 πn, x = - 0.46364 \dots + 2 πn, x = π + 0.46364 \dots + 2 πn

+1

度数

x = 26.56505 \dots^{\circ} + 36 0^{\circ} n, x = 153.43494 \dots^{\circ} + 36 0^{\circ} n, x = - 26.56505 \dots^{\circ} + 36 0^{\circ} n, x = 206.56505 \dots^{\circ} + 36 0^{\circ} n

求解步骤

sin^{2} (x) = 0.2

用替代法求解

sin^{2} (x) = 0.2

令

: sin (x) = u

u^{2} = 0.2

u^{2} = 0.2 : u = 0.2, u = - 0.2

u^{2} = 0.2

对于

x^{2} = f (a)

解为

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

u = 0.2, u = - 0.2

u = sin (x)

代回

sin (x) = 0.2, sin (x) = - 0.2

sin (x) = 0.2, sin (x) = - 0.2

sin (x) = 0.2 : x = arcsin (0.2) + 2 πn, x = π - arcsin (0.2) + 2 πn

sin (x) = 0.2

使用反三角函数性质

sin (x) = 0.2

sin (x) = 0.2

的通解

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

x = arcsin (0.2) + 2 πn, x = π - arcsin (0.2) + 2 πn

x = arcsin (0.2) + 2 πn, x = π - arcsin (0.2) + 2 πn

sin (x) = - 0.2 : x = arcsin (- 0.2) + 2 πn, x = π + arcsin (0.2) + 2 πn

sin (x) = - 0.2

使用反三角函数性质

sin (x) = - 0.2

sin (x) = - 0.2

的通解

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

x = arcsin (- 0.2) + 2 πn, x = π + arcsin (0.2) + 2 πn

x = arcsin (- 0.2) + 2 πn, x = π + arcsin (0.2) + 2 πn

合并所有解

x = arcsin (0.2) + 2 πn, x = π - arcsin (0.2) + 2 πn, x = arcsin (- 0.2) + 2 πn, x = π + arcsin (0.2) + 2 πn

以小数形式表示解

x = 0.46364 \dots + 2 πn, x = π - 0.46364 \dots + 2 πn, x = - 0.46364 \dots + 2 πn, x = π + 0.46364 \dots + 2 πn

作图

流行的例子

sin(x)=(sin(45))/(1.3)

sin (x) = \frac{sin ( 4 5 ^{\circ} )}{1.3}

arctan(x)+arctan(1-x)=arctan(9/7)

arctan (x) + arctan (1 - x) = arctan (\frac{9}{7})

(2cos(x)+1)(sin(x)-1)=0

(2 cos (x) + 1) (sin (x) - 1) = 0

3cos^2(θ)-sin^2(θ)=0

3 cos^{2} (θ) - sin^{2} (θ) = 0

sin(x)=((sqrt(6))/4)

sin (x) = (\frac{6}{4})