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受欢迎的三角函数 >

-3sin(3x)=1

解答

- 3 sin (3 x) = 1

解答

x = - \frac{0.33983 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} + \frac{0.33983 \dots}{3} + \frac{2 πn}{3}

+1

度数

x = - 6.49040 \dots^{\circ} + 12 0^{\circ} n, x = 66.49040 \dots^{\circ} + 12 0^{\circ} n

求解步骤

- 3 sin (3 x) = 1

两边除以

- 3

- 3 sin (3 x) = 1

两边除以

- 3

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

化简

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

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

使用反三角函数性质

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

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

的通解

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

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

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

解

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

3 x = arcsin (- \frac{1}{3}) + 2 πn

化简

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

arcsin (- \frac{1}{3}) + 2 πn

利用以下特性:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{1}{3}) = - arcsin (\frac{1}{3})

= - arcsin (\frac{1}{3}) + 2 πn

3 x = - arcsin (\frac{1}{3}) + 2 πn

两边除以

3

3 x = - arcsin (\frac{1}{3}) + 2 πn

两边除以

3

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

化简

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

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

解

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

3 x = π + arcsin (\frac{1}{3}) + 2 πn

两边除以

3

3 x = π + arcsin (\frac{1}{3}) + 2 πn

两边除以

3

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

化简

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

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

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

以小数形式表示解

x = - \frac{0.33983 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} + \frac{0.33983 \dots}{3} + \frac{2 πn}{3}

作图

流行的例子

cos(θ)= 3/5 (270360)

2sin(x)=tan(x)cos(x)-cos(x)

cos(θ)-sin(θ)=1,0<= θ<= 2pi