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 >

solvefor x,Y=0.5sin(3.07x-2.4t+0.59)

解答

求解

x, Y = 0.5 sin (3.07 x - 2.4 t + 0.59)

解答

x = \frac{arcsin ( 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}, x = \frac{π}{3.07} + \frac{arcsin ( - 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}

求解步骤

Y = 0.5 sin (3.07 x - 2.4 t + 0.59)

交换两边

0.5 sin (3.07 x - 2.4 t + 0.59) = Y

在两边乘以

10

0.5 sin (3.07 x - 2.4 t + 0.59) = Y

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

0.5 sin (3.07 x - 2.4 t + 0.59) \cdot 10 = Y \cdot 10

整理后得

5 sin (3.07 x - 2.4 t + 0.59) = Y \cdot 10

5 sin (3.07 x - 2.4 t + 0.59) = Y \cdot 10

两边除以

5

5 sin (3.07 x - 2.4 t + 0.59) = Y \cdot 10

两边除以

5

\frac{5 sin ( 3.07 x - 2.4 t + 0.59 )}{5} = \frac{Y \cdot 10}{5}

化简

sin (3.07 x - 2.4 t + 0.59) = 2 Y

sin (3.07 x - 2.4 t + 0.59) = 2 Y

使用反三角函数性质

sin (3.07 x - 2.4 t + 0.59) = 2 Y

sin (3.07 x - 2.4 t + 0.59) = 2 Y

的通解

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

3.07 x - 2.4 t + 0.59 = arcsin (2 Y) + 2 πn, 3.07 x - 2.4 t + 0.59 = π + arcsin (- 2 Y) + 2 πn

3.07 x - 2.4 t + 0.59 = arcsin (2 Y) + 2 πn, 3.07 x - 2.4 t + 0.59 = π + arcsin (- 2 Y) + 2 πn

解

3.07 x - 2.4 t + 0.59 = arcsin (2 Y) + 2 πn : x = \frac{arcsin ( 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}

3.07 x - 2.4 t + 0.59 = arcsin (2 Y) + 2 πn

将

2.4 t

到右边

3.07 x - 2.4 t + 0.59 = arcsin (2 Y) + 2 πn

两边加上

2.4 t

3.07 x - 2.4 t + 0.59 + 2.4 t = arcsin (2 Y) + 2 πn + 2.4 t

化简

3.07 x + 0.59 = arcsin (2 Y) + 2 πn + 2.4 t

3.07 x + 0.59 = arcsin (2 Y) + 2 πn + 2.4 t

将

0.59

到右边

3.07 x + 0.59 = arcsin (2 Y) + 2 πn + 2.4 t

两边减去

0.59

3.07 x + 0.59 - 0.59 = arcsin (2 Y) + 2 πn + 2.4 t - 0.59

化简

3.07 x = arcsin (2 Y) + 2 πn + 2.4 t - 0.59

3.07 x = arcsin (2 Y) + 2 πn + 2.4 t - 0.59

两边除以

3.07

3.07 x = arcsin (2 Y) + 2 πn + 2.4 t - 0.59

两边除以

3.07

\frac{3.07 x}{3.07} = \frac{arcsin ( 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}

化简

x = \frac{arcsin ( 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}

x = \frac{arcsin ( 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}

解

3.07 x - 2.4 t + 0.59 = π + arcsin (- 2 Y) + 2 πn : x = \frac{π}{3.07} + \frac{arcsin ( - 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}

3.07 x - 2.4 t + 0.59 = π + arcsin (- 2 Y) + 2 πn

将

2.4 t

到右边

3.07 x - 2.4 t + 0.59 = π + arcsin (- 2 Y) + 2 πn

两边加上

2.4 t

3.07 x - 2.4 t + 0.59 + 2.4 t = π + arcsin (- 2 Y) + 2 πn + 2.4 t

化简

3.07 x + 0.59 = π + arcsin (- 2 Y) + 2 πn + 2.4 t

3.07 x + 0.59 = π + arcsin (- 2 Y) + 2 πn + 2.4 t

将

0.59

到右边

3.07 x + 0.59 = π + arcsin (- 2 Y) + 2 πn + 2.4 t

两边减去

0.59

3.07 x + 0.59 - 0.59 = π + arcsin (- 2 Y) + 2 πn + 2.4 t - 0.59

化简

3.07 x = π + arcsin (- 2 Y) + 2 πn + 2.4 t - 0.59

3.07 x = π + arcsin (- 2 Y) + 2 πn + 2.4 t - 0.59

两边除以

3.07

3.07 x = π + arcsin (- 2 Y) + 2 πn + 2.4 t - 0.59

两边除以

3.07

\frac{3.07 x}{3.07} = \frac{π}{3.07} + \frac{arcsin ( - 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}

化简

x = \frac{π}{3.07} + \frac{arcsin ( - 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}

x = \frac{π}{3.07} + \frac{arcsin ( - 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}

x = \frac{arcsin ( 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}, x = \frac{π}{3.07} + \frac{arcsin ( - 2 Y )}{3.07} + \frac{2 πn}{3.07} + \frac{2.4 t}{3.07} - \frac{0.59}{3.07}

作图

流行的例子

sin(x-30)cos(x-30)=(sqrt(3))/4

sin (x - 3 0^{\circ}) cos (x - 3 0^{\circ}) = \frac{3}{4}

cos(θ)=-7/15 ,cos(θ/2),180<θ<270

cos (θ) = - \frac{7}{15}, cos (\frac{θ}{2}), 18 0^{\circ} < θ < 27 0^{\circ}

tan (\frac{x}{2}) = 4

-2sin(x)=-sqrt(2)

- 2 sin (x) = - 2

sin(pi-x)=cos((3pi)/2-x)+cos(pi)

sin (π - x) = cos (\frac{3 π}{2} - x) + cos (π)