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 >

8/17 =sin(2x)

解答

\frac{8}{17} = sin (2 x)

解答

x = \frac{0.48995 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.48995 \dots}{2} + πn

+1

度数

x = 14.03624 \dots^{\circ} + 18 0^{\circ} n, x = 75.96375 \dots^{\circ} + 18 0^{\circ} n

求解步骤

\frac{8}{17} = sin (2 x)

交换两边

sin (2 x) = \frac{8}{17}

使用反三角函数性质

sin (2 x) = \frac{8}{17}

sin (2 x) = \frac{8}{17}

的通解

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

2 x = arcsin (\frac{8}{17}) + 2 πn, 2 x = π - arcsin (\frac{8}{17}) + 2 πn

2 x = arcsin (\frac{8}{17}) + 2 πn, 2 x = π - arcsin (\frac{8}{17}) + 2 πn

解

2 x = arcsin (\frac{8}{17}) + 2 πn : x = \frac{arcsin ( \frac{8}{17} )}{2} + πn

2 x = arcsin (\frac{8}{17}) + 2 πn

两边除以

2

2 x = arcsin (\frac{8}{17}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{arcsin ( \frac{8}{17} )}{2} + \frac{2 πn}{2}

化简

x = \frac{arcsin ( \frac{8}{17} )}{2} + πn

x = \frac{arcsin ( \frac{8}{17} )}{2} + πn

解

2 x = π - arcsin (\frac{8}{17}) + 2 πn : x = \frac{π}{2} - \frac{arcsin ( \frac{8}{17} )}{2} + πn

2 x = π - arcsin (\frac{8}{17}) + 2 πn

两边除以

2

2 x = π - arcsin (\frac{8}{17}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( \frac{8}{17} )}{2} + \frac{2 πn}{2}

化简

x = \frac{π}{2} - \frac{arcsin ( \frac{8}{17} )}{2} + πn

x = \frac{π}{2} - \frac{arcsin ( \frac{8}{17} )}{2} + πn

x = \frac{arcsin ( \frac{8}{17} )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( \frac{8}{17} )}{2} + πn

以小数形式表示解

x = \frac{0.48995 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.48995 \dots}{2} + πn

作图

流行的例子

sec(2x)+tan(2x)=2

sec (2 x) + tan (2 x) = 2

sec(2x)+tan(2x)=9

sec (2 x) + tan (2 x) = 9

tan(4x)-tan(2x)=0

tan (4 x) - tan (2 x) = 0

solvefor t,sin(t)+2sin(2t)=0

so l v e f or t, sin (t) + 2 sin (2 t) = 0

tan^2(x)-sin(x)tan^2(x)=0

tan^{2} (x) - sin (x) tan^{2} (x) = 0