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0=3sin(x-1/2 pi)+2

解答

0 = 3 sin (x - \frac{1}{2} π) + 2

解答

x = - 0.72972 \dots + 2 πn + \frac{π}{2}, x = π + 0.72972 \dots + 2 πn + \frac{π}{2}

+1

度数

x = 48.18968 \dots^{\circ} + 36 0^{\circ} n, x = 311.81031 \dots^{\circ} + 36 0^{\circ} n

求解步骤

0 = 3 sin (x - \frac{1}{2} π) + 2

交换两边

3 sin (x - \frac{1}{2} π) + 2 = 0

将

2

到右边

3 sin (x - \frac{1}{2} π) + 2 = 0

两边减去

2

3 sin (x - \frac{1}{2} π) + 2 - 2 = 0 - 2

化简

3 sin (x - \frac{1}{2} π) = - 2

3 sin (x - \frac{1}{2} π) = - 2

两边除以

3

3 sin (x - \frac{1}{2} π) = - 2

两边除以

3

\frac{3 sin ( x - \frac{1}{2} π )}{3} = \frac{- 2}{3}

化简

sin (x - \frac{1}{2} π) = - \frac{2}{3}

sin (x - \frac{1}{2} π) = - \frac{2}{3}

使用反三角函数性质

sin (x - \frac{1}{2} π) = - \frac{2}{3}

sin (x - \frac{1}{2} π) = - \frac{2}{3}

的通解

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

x - \frac{1}{2} π = arcsin (- \frac{2}{3}) + 2 πn, x - \frac{1}{2} π = π + arcsin (\frac{2}{3}) + 2 πn

x - \frac{1}{2} π = arcsin (- \frac{2}{3}) + 2 πn, x - \frac{1}{2} π = π + arcsin (\frac{2}{3}) + 2 πn

解

x - \frac{1}{2} π = arcsin (- \frac{2}{3}) + 2 πn : x = - arcsin (\frac{2}{3}) + 2 πn + \frac{π}{2}

x - \frac{1}{2} π = arcsin (- \frac{2}{3}) + 2 πn

化简

x - \frac{1}{2} π : x - \frac{π}{2}

x - \frac{1}{2} π

\frac{1}{2} π = \frac{π}{2}

\frac{1}{2} π

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 π}{2}

乘以:

1 π = π

= \frac{π}{2}

= x - \frac{π}{2}

化简

arcsin (- \frac{2}{3}) + 2 πn : - arcsin (\frac{2}{3}) + 2 πn

arcsin (- \frac{2}{3}) + 2 πn

利用以下特性:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{2}{3}) = - arcsin (\frac{2}{3})

= - arcsin (\frac{2}{3}) + 2 πn

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

将

\frac{π}{2}

到右边

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

两边加上

\frac{π}{2}

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

化简

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

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

解

x - \frac{1}{2} π = π + arcsin (\frac{2}{3}) + 2 πn : x = π + arcsin (\frac{2}{3}) + 2 πn + \frac{π}{2}

x - \frac{1}{2} π = π + arcsin (\frac{2}{3}) + 2 πn

\frac{1}{2} π = \frac{π}{2}

\frac{1}{2} π

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 π}{2}

乘以:

1 π = π

= \frac{π}{2}

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

将

\frac{π}{2}

到右边

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

两边加上

\frac{π}{2}

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

化简

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

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

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

以小数形式表示解

x = - 0.72972 \dots + 2 πn + \frac{π}{2}, x = π + 0.72972 \dots + 2 πn + \frac{π}{2}

流行的例子

2sin^2(x)=3sin(x)

2 sin^{2} (x) = 3 sin (x)

5 + 2 sin (x) - 7 = 0

0 = 4 sin (4 x + 3 π)

0.5 = 1 - sin (θ)

solvefor θ,r=6sin(2θ)求解

θ, r = 6 sin (2 θ)