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受欢迎的三角函数 >

-4sin(x)=4(sin(x)-1)

解答

- 4 sin (x) = 4 (sin (x) - 1)

解答

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

+1

度数

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

求解步骤

- 4 sin (x) = 4 (sin (x) - 1)

用替代法求解

- 4 sin (x) = 4 (sin (x) - 1)

令

: sin (x) = u

- 4 u = 4 (u - 1)

- 4 u = 4 (u - 1) : u = \frac{1}{2}

- 4 u = 4 (u - 1)

展开

4 (u - 1) : 4 u - 4

4 (u - 1)

使用分配律:

a (b - c) = ab - a c

a = 4, b = u, c = 1

= 4 u - 4 \cdot 1

数字相乘:

4 \cdot 1 = 4

= 4 u - 4

- 4 u = 4 u - 4

将

4 u

para o lado esquerdo

- 4 u = 4 u - 4

两边减去

4 u

- 4 u - 4 u = 4 u - 4 - 4 u

化简

- 8 u = - 4

- 8 u = - 4

两边除以

- 8

- 8 u = - 4

两边除以

- 8

\frac{- 8 u}{- 8} = \frac{- 4}{- 8}

化简

\frac{- 8 u}{- 8} = \frac{- 4}{- 8}

化简

\frac{- 8 u}{- 8} : u

\frac{- 8 u}{- 8}

使用分式法则:

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

= \frac{8 u}{8}

数字相除:

\frac{8}{8} = 1

= u

化简

\frac{- 4}{- 8} : \frac{1}{2}

\frac{- 4}{- 8}

使用分式法则:

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

= \frac{4}{8}

约分:

4

= \frac{1}{2}

u = \frac{1}{2}

u = \frac{1}{2}

u = \frac{1}{2}

u = sin (x)

代回

sin (x) = \frac{1}{2}

sin (x) = \frac{1}{2}

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

sin (x) = \frac{1}{2}

sin (x) = \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}

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

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

合并所有解

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

作图

流行的例子

3/(tan(x))=(2tan(x))(2cos(x))

\frac{3}{tan ( x )} = (2 tan (x)) (2 cos (x))

cos(θ)=-4/5 ,sin(θ)

cos (θ) = - \frac{4}{5}, sin (θ)

5sin(4x)=4cos(2x)

5 sin (4 x) = 4 cos (2 x)

arccosh (x) = 1

solvefor θ,sin(3θ)= 1/2

so l v e f or θ, sin (3 θ) = \frac{1}{2}