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(3θ-15)=0.7

解答

sin (3 θ - 15) = 0.7

解答

θ = 5 + \frac{2 πn}{3} + \frac{0.77539 \dots}{3}, θ = \frac{π}{3} + \frac{2 πn}{3} - \frac{0.77539 \dots}{3} + 5

+1

度数

θ = 301.28789 \dots^{\circ} + 12 0^{\circ} n, θ = 331.66989 \dots^{\circ} + 12 0^{\circ} n

求解步骤

sin (3 θ - 15) = 0.7

使用反三角函数性质

sin (3 θ - 15) = 0.7

sin (3 θ - 15) = 0.7

的通解

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

3 θ - 15 = arcsin (0.7) + 2 πn, 3 θ - 15 = π - arcsin (0.7) + 2 πn

3 θ - 15 = arcsin (0.7) + 2 πn, 3 θ - 15 = π - arcsin (0.7) + 2 πn

解

3 θ - 15 = arcsin (0.7) + 2 πn : θ = 5 + \frac{2 πn}{3} + \frac{arcsin ( 0.7 )}{3}

3 θ - 15 = arcsin (0.7) + 2 πn

将

15

到右边

3 θ - 15 = arcsin (0.7) + 2 πn

两边加上

15

3 θ - 15 + 15 = arcsin (0.7) + 2 πn + 15

化简

3 θ = arcsin (0.7) + 2 πn + 15

3 θ = arcsin (0.7) + 2 πn + 15

两边除以

3

3 θ = arcsin (0.7) + 2 πn + 15

两边除以

3

\frac{3 θ}{3} = \frac{arcsin ( 0.7 )}{3} + \frac{2 πn}{3} + \frac{15}{3}

化简

\frac{3 θ}{3} = \frac{arcsin ( 0.7 )}{3} + \frac{2 πn}{3} + \frac{15}{3}

化简

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

数字相除:

\frac{3}{3} = 1

= θ

化简

\frac{arcsin ( 0.7 )}{3} + \frac{2 πn}{3} + \frac{15}{3} : 5 + \frac{2 πn}{3} + \frac{arcsin ( 0.7 )}{3}

\frac{arcsin ( 0.7 )}{3} + \frac{2 πn}{3} + \frac{15}{3}

对同类项分组

= \frac{15}{3} + \frac{2 πn}{3} + \frac{arcsin ( 0.7 )}{3}

数字相除:

\frac{15}{3} = 5

= 5 + \frac{2 πn}{3} + \frac{arcsin ( 0.7 )}{3}

θ = 5 + \frac{2 πn}{3} + \frac{arcsin ( 0.7 )}{3}

θ = 5 + \frac{2 πn}{3} + \frac{arcsin ( 0.7 )}{3}

θ = 5 + \frac{2 πn}{3} + \frac{arcsin ( 0.7 )}{3}

解

3 θ - 15 = π - arcsin (0.7) + 2 πn : θ = \frac{π}{3} + \frac{2 πn}{3} - \frac{arcsin ( 0.7 )}{3} + 5

3 θ - 15 = π - arcsin (0.7) + 2 πn

将

15

到右边

3 θ - 15 = π - arcsin (0.7) + 2 πn

两边加上

15

3 θ - 15 + 15 = π - arcsin (0.7) + 2 πn + 15

化简

3 θ = π - arcsin (0.7) + 2 πn + 15

3 θ = π - arcsin (0.7) + 2 πn + 15

两边除以

3

3 θ = π - arcsin (0.7) + 2 πn + 15

两边除以

3

\frac{3 θ}{3} = \frac{π}{3} - \frac{arcsin ( 0.7 )}{3} + \frac{2 πn}{3} + \frac{15}{3}

化简

\frac{3 θ}{3} = \frac{π}{3} - \frac{arcsin ( 0.7 )}{3} + \frac{2 πn}{3} + \frac{15}{3}

化简

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

数字相除:

\frac{3}{3} = 1

= θ

化简

\frac{π}{3} - \frac{arcsin ( 0.7 )}{3} + \frac{2 πn}{3} + \frac{15}{3} : \frac{π}{3} + \frac{2 πn}{3} - \frac{arcsin ( 0.7 )}{3} + 5

\frac{π}{3} - \frac{arcsin ( 0.7 )}{3} + \frac{2 πn}{3} + \frac{15}{3}

对同类项分组

= \frac{π}{3} + \frac{15}{3} + \frac{2 πn}{3} - \frac{arcsin ( 0.7 )}{3}

数字相除:

\frac{15}{3} = 5

= \frac{π}{3} + 5 + \frac{2 πn}{3} - \frac{arcsin ( 0.7 )}{3}

对同类项分组

= \frac{π}{3} + \frac{2 πn}{3} - \frac{arcsin ( 0.7 )}{3} + 5

θ = \frac{π}{3} + \frac{2 πn}{3} - \frac{arcsin ( 0.7 )}{3} + 5

θ = \frac{π}{3} + \frac{2 πn}{3} - \frac{arcsin ( 0.7 )}{3} + 5

θ = \frac{π}{3} + \frac{2 πn}{3} - \frac{arcsin ( 0.7 )}{3} + 5

θ = 5 + \frac{2 πn}{3} + \frac{arcsin ( 0.7 )}{3}, θ = \frac{π}{3} + \frac{2 πn}{3} - \frac{arcsin ( 0.7 )}{3} + 5

以小数形式表示解

θ = 5 + \frac{2 πn}{3} + \frac{0.77539 \dots}{3}, θ = \frac{π}{3} + \frac{2 πn}{3} - \frac{0.77539 \dots}{3} + 5

作图

流行的例子

tan (x - \frac{π}{6}) = 1

cos^2(x)+((1-sqrt(2))/2)cos(x)-(sqrt(2))/4 =0

cos^{2} (x) + (\frac{1 - 2}{2}) cos (x) - \frac{2}{4} = 0

tan^{2} (\frac{x}{2}) = - 2

sin^2(θ)-1=2sin(θ)

sin^{2} (θ) - 1 = 2 sin (θ)

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