zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的 >

r=asin(3x)

解答

r = a sin (3 x)

解答

x = \frac{arcsin ( \frac{r}{a} )}{3} + \frac{2 πn}{3}, x = \frac{π}{3} + \frac{arcsin ( - \frac{r}{a} )}{3} + \frac{2 πn}{3}

求解步骤

r = a sin (3 x)

交换两边

a sin (3 x) = r

两边除以

a; a \neq = 0

a sin (3 x) = r

两边除以

a; a \neq = 0

\frac{a sin ( 3 x )}{a} = \frac{r}{a}; a \neq = 0

化简

sin (3 x) = \frac{r}{a}; a \neq = 0

sin (3 x) = \frac{r}{a}; a \neq = 0

使用反三角函数性质

sin (3 x) = \frac{r}{a}

sin (3 x) = \frac{r}{a}

的通解

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

3 x = arcsin (\frac{r}{a}) + 2 πn, 3 x = π + arcsin (- \frac{r}{a}) + 2 πn

3 x = arcsin (\frac{r}{a}) + 2 πn, 3 x = π + arcsin (- \frac{r}{a}) + 2 πn

解

3 x = arcsin (\frac{r}{a}) + 2 πn : x = \frac{arcsin ( \frac{r}{a} )}{3} + \frac{2 πn}{3}

3 x = arcsin (\frac{r}{a}) + 2 πn

两边除以

3

3 x = arcsin (\frac{r}{a}) + 2 πn

两边除以

3

\frac{3 x}{3} = \frac{arcsin ( \frac{r}{a} )}{3} + \frac{2 πn}{3}

化简

x = \frac{arcsin ( \frac{r}{a} )}{3} + \frac{2 πn}{3}

x = \frac{arcsin ( \frac{r}{a} )}{3} + \frac{2 πn}{3}

解

3 x = π + arcsin (- \frac{r}{a}) + 2 πn : x = \frac{π}{3} + \frac{arcsin ( - \frac{r}{a} )}{3} + \frac{2 πn}{3}

3 x = π + arcsin (- \frac{r}{a}) + 2 πn

两边除以

3

3 x = π + arcsin (- \frac{r}{a}) + 2 πn

两边除以

3

\frac{3 x}{3} = \frac{π}{3} + \frac{arcsin ( - \frac{r}{a} )}{3} + \frac{2 πn}{3}

化简

x = \frac{π}{3} + \frac{arcsin ( - \frac{r}{a} )}{3} + \frac{2 πn}{3}

x = \frac{π}{3} + \frac{arcsin ( - \frac{r}{a} )}{3} + \frac{2 πn}{3}

x = \frac{arcsin ( \frac{r}{a} )}{3} + \frac{2 πn}{3}, x = \frac{π}{3} + \frac{arcsin ( - \frac{r}{a} )}{3} + \frac{2 πn}{3}

流行的例子

sin (x) = \frac{18}{25}

3cos(x)-sin^2(x)+3=0

3 cos (x) - sin^{2} (x) + 3 = 0

solvefor x,cos(x)= 1/4 求解

x, cos (x) = \frac{1}{4}

cos^{2} (t) = 0

sin (x) = \frac{18}{12}