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 >

35+53sin(2T-31.9)=0

解答

35 + 53 sin (2 T - 31.9) = 0

解答

T = πn + \frac{31.9}{2} - \frac{0.72132 \dots}{2}, T = πn + \frac{π}{2} + \frac{31.9}{2} + \frac{0.72132 \dots}{2}

+1

度数

T = 893.20335 \dots^{\circ} + 18 0^{\circ} n, T = 1024.53201 \dots^{\circ} + 18 0^{\circ} n

求解步骤

35 + 53 sin (2 T - 31.9) = 0

将

35

到右边

35 + 53 sin (2 T - 31.9) = 0

两边减去

35

35 + 53 sin (2 T - 31.9) - 35 = 0 - 35

化简

53 sin (2 T - 31.9) = - 35

53 sin (2 T - 31.9) = - 35

两边除以

53

53 sin (2 T - 31.9) = - 35

两边除以

53

\frac{53 sin ( 2 T - 31.9 )}{53} = \frac{- 35}{53}

化简

sin (2 T - 31.9) = - \frac{35}{53}

sin (2 T - 31.9) = - \frac{35}{53}

使用反三角函数性质

sin (2 T - 31.9) = - \frac{35}{53}

sin (2 T - 31.9) = - \frac{35}{53}

的通解

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

2 T - 31.9 = arcsin (- \frac{35}{53}) + 2 πn, 2 T - 31.9 = π + arcsin (\frac{35}{53}) + 2 πn

2 T - 31.9 = arcsin (- \frac{35}{53}) + 2 πn, 2 T - 31.9 = π + arcsin (\frac{35}{53}) + 2 πn

解

2 T - 31.9 = arcsin (- \frac{35}{53}) + 2 πn : T = πn + \frac{31.9}{2} - \frac{arcsin ( \frac{35}{53} )}{2}

2 T - 31.9 = arcsin (- \frac{35}{53}) + 2 πn

化简

arcsin (- \frac{35}{53}) + 2 πn : - arcsin (\frac{35}{53}) + 2 πn

arcsin (- \frac{35}{53}) + 2 πn

利用以下特性:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{35}{53}) = - arcsin (\frac{35}{53})

= - arcsin (\frac{35}{53}) + 2 πn

2 T - 31.9 = - arcsin (\frac{35}{53}) + 2 πn

将

31.9

到右边

2 T - 31.9 = - arcsin (\frac{35}{53}) + 2 πn

两边加上

31.9

2 T - 31.9 + 31.9 = - arcsin (\frac{35}{53}) + 2 πn + 31.9

化简

2 T = - arcsin (\frac{35}{53}) + 2 πn + 31.9

2 T = - arcsin (\frac{35}{53}) + 2 πn + 31.9

两边除以

2

2 T = - arcsin (\frac{35}{53}) + 2 πn + 31.9

两边除以

2

\frac{2 T}{2} = - \frac{arcsin ( \frac{35}{53} )}{2} + \frac{2 πn}{2} + \frac{31.9}{2}

化简

\frac{2 T}{2} = - \frac{arcsin ( \frac{35}{53} )}{2} + \frac{2 πn}{2} + \frac{31.9}{2}

化简

\frac{2 T}{2} : T

\frac{2 T}{2}

数字相除:

\frac{2}{2} = 1

= T

化简

- \frac{arcsin ( \frac{35}{53} )}{2} + \frac{2 πn}{2} + \frac{31.9}{2} : πn + \frac{31.9}{2} - \frac{arcsin ( \frac{35}{53} )}{2}

- \frac{arcsin ( \frac{35}{53} )}{2} + \frac{2 πn}{2} + \frac{31.9}{2}

对同类项分组

= \frac{31.9}{2} + \frac{2 πn}{2} - \frac{arcsin ( \frac{35}{53} )}{2}

数字相除:

\frac{2}{2} = 1

= \frac{31.9}{2} + πn - \frac{arcsin ( \frac{35}{53} )}{2}

对同类项分组

= πn + \frac{31.9}{2} - \frac{arcsin ( \frac{35}{53} )}{2}

T = πn + \frac{31.9}{2} - \frac{arcsin ( \frac{35}{53} )}{2}

T = πn + \frac{31.9}{2} - \frac{arcsin ( \frac{35}{53} )}{2}

T = πn + \frac{31.9}{2} - \frac{arcsin ( \frac{35}{53} )}{2}

解

2 T - 31.9 = π + arcsin (\frac{35}{53}) + 2 πn : T = πn + \frac{π}{2} + \frac{31.9}{2} + \frac{arcsin ( \frac{35}{53} )}{2}

2 T - 31.9 = π + arcsin (\frac{35}{53}) + 2 πn

将

31.9

到右边

2 T - 31.9 = π + arcsin (\frac{35}{53}) + 2 πn

两边加上

31.9

2 T - 31.9 + 31.9 = π + arcsin (\frac{35}{53}) + 2 πn + 31.9

化简

2 T = π + arcsin (\frac{35}{53}) + 2 πn + 31.9

2 T = π + arcsin (\frac{35}{53}) + 2 πn + 31.9

两边除以

2

2 T = π + arcsin (\frac{35}{53}) + 2 πn + 31.9

两边除以

2

\frac{2 T}{2} = \frac{π}{2} + \frac{arcsin ( \frac{35}{53} )}{2} + \frac{2 πn}{2} + \frac{31.9}{2}

化简

\frac{2 T}{2} = \frac{π}{2} + \frac{arcsin ( \frac{35}{53} )}{2} + \frac{2 πn}{2} + \frac{31.9}{2}

化简

\frac{2 T}{2} : T

\frac{2 T}{2}

数字相除:

\frac{2}{2} = 1

= T

化简

\frac{π}{2} + \frac{arcsin ( \frac{35}{53} )}{2} + \frac{2 πn}{2} + \frac{31.9}{2} : πn + \frac{π}{2} + \frac{31.9}{2} + \frac{arcsin ( \frac{35}{53} )}{2}

\frac{π}{2} + \frac{arcsin ( \frac{35}{53} )}{2} + \frac{2 πn}{2} + \frac{31.9}{2}

对同类项分组

= \frac{π}{2} + \frac{31.9}{2} + \frac{2 πn}{2} + \frac{arcsin ( \frac{35}{53} )}{2}

数字相除:

\frac{2}{2} = 1

= \frac{π}{2} + \frac{31.9}{2} + πn + \frac{arcsin ( \frac{35}{53} )}{2}

对同类项分组

= πn + \frac{π}{2} + \frac{31.9}{2} + \frac{arcsin ( \frac{35}{53} )}{2}

T = πn + \frac{π}{2} + \frac{31.9}{2} + \frac{arcsin ( \frac{35}{53} )}{2}

T = πn + \frac{π}{2} + \frac{31.9}{2} + \frac{arcsin ( \frac{35}{53} )}{2}

T = πn + \frac{π}{2} + \frac{31.9}{2} + \frac{arcsin ( \frac{35}{53} )}{2}

T = πn + \frac{31.9}{2} - \frac{arcsin ( \frac{35}{53} )}{2}, T = πn + \frac{π}{2} + \frac{31.9}{2} + \frac{arcsin ( \frac{35}{53} )}{2}

以小数形式表示解

T = πn + \frac{31.9}{2} - \frac{0.72132 \dots}{2}, T = πn + \frac{π}{2} + \frac{31.9}{2} + \frac{0.72132 \dots}{2}

作图

流行的例子

cos (2 x) = - 12

sin(x)= 1/3 ,cos(x)

sin (x) = \frac{1}{3}, cos (x)

sec(2x-10)=csc(32)

sec (2 x - 1 0^{\circ}) = csc (3 2^{\circ})

4 = cos (x)

solvefor x,e^{4y}=cos(4x+y)

so l v e f or x, e^{4 y} = cos (4 x + y)