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受欢迎的三角函数 >

3+3sin(θ)=9sin(θ)

解答

3 + 3 sin (θ) = 9 sin (θ)

解答

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

+1

度数

θ = 3 0^{\circ} + 36 0^{\circ} n, θ = 15 0^{\circ} + 36 0^{\circ} n

求解步骤

3 + 3 sin (θ) = 9 sin (θ)

用替代法求解

3 + 3 sin (θ) = 9 sin (θ)

令

: sin (θ) = u

3 + 3 u = 9 u

3 + 3 u = 9 u : u = \frac{1}{2}

3 + 3 u = 9 u

将

3

到右边

3 + 3 u = 9 u

两边减去

3

3 + 3 u - 3 = 9 u - 3

化简

3 u = 9 u - 3

3 u = 9 u - 3

将

9 u

para o lado esquerdo

3 u = 9 u - 3

两边减去

9 u

3 u - 9 u = 9 u - 3 - 9 u

化简

- 6 u = - 3

- 6 u = - 3

两边除以

- 6

- 6 u = - 3

两边除以

- 6

\frac{- 6 u}{- 6} = \frac{- 3}{- 6}

化简

\frac{- 6 u}{- 6} = \frac{- 3}{- 6}

化简

\frac{- 6 u}{- 6} : u

\frac{- 6 u}{- 6}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

= \frac{6 u}{6}

数字相除:

\frac{6}{6} = 1

= u

化简

\frac{- 3}{- 6} : \frac{1}{2}

\frac{- 3}{- 6}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

= \frac{3}{6}

约分:

3

= \frac{1}{2}

u = \frac{1}{2}

u = \frac{1}{2}

u = \frac{1}{2}

u = sin (θ)

代回

sin (θ) = \frac{1}{2}

sin (θ) = \frac{1}{2}

sin (θ) = \frac{1}{2} : θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

sin (θ) = \frac{1}{2}

sin (θ) = \frac{1}{2}

的通解

sin (x)

周期表（周期为

2 πn

"）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

合并所有解

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

作图

流行的例子

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