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受欢迎的三角函数 >

2sin(x)+(sqrt(3))/4 = 3/2 sin(x)

解答

2 sin (x) + \frac{3}{4} = \frac{3}{2} sin (x)

解答

x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

+1

度数

x = 24 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

求解步骤

2 sin (x) + \frac{3}{4} = \frac{3}{2} sin (x)

用替代法求解

2 sin (x) + \frac{3}{4} = \frac{3}{2} sin (x)

令

: sin (x) = u

2 u + \frac{3}{4} = \frac{3}{2} u

2 u + \frac{3}{4} = \frac{3}{2} u : u = - \frac{3}{2}

2 u + \frac{3}{4} = \frac{3}{2} u

将

\frac{3}{4}

到右边

2 u + \frac{3}{4} = \frac{3}{2} u

两边减去

\frac{3}{4}

2 u + \frac{3}{4} - \frac{3}{4} = \frac{3}{2} u - \frac{3}{4}

化简

2 u = \frac{3}{2} u - \frac{3}{4}

2 u = \frac{3}{2} u - \frac{3}{4}

将

\frac{3}{2} u

para o lado esquerdo

2 u = \frac{3}{2} u - \frac{3}{4}

两边减去

\frac{3}{2} u

2 u - \frac{3}{2} u = \frac{3}{2} u - \frac{3}{4} - \frac{3}{2} u

化简

2 u - \frac{3}{2} u = \frac{3}{2} u - \frac{3}{4} - \frac{3}{2} u

化简

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

2 u - \frac{3}{2} u

因式分解出通项

u

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

2 - \frac{3}{2} = \frac{1}{2}

2 - \frac{3}{2}

将项转换为分式:

2 = \frac{2 \cdot 2}{2}

= \frac{2 \cdot 2}{2} - \frac{3}{2}

因为分母相等，所以合并分式:

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

= \frac{2 \cdot 2 - 3}{2}

2 \cdot 2 - 3 = 1

2 \cdot 2 - 3

数字相乘:

2 \cdot 2 = 4

= 4 - 3

数字相减:

4 - 3 = 1

= 1

= \frac{1}{2}

= \frac{1}{2} u

化简

\frac{3}{2} u - \frac{3}{4} - \frac{3}{2} u : - \frac{3}{4}

\frac{3}{2} u - \frac{3}{4} - \frac{3}{2} u

同类项相加:

\frac{3}{2} u - \frac{3}{2} u = 0

= - \frac{3}{4}

\frac{1}{2} u = - \frac{3}{4}

\frac{1}{2} u = - \frac{3}{4}

\frac{1}{2} u = - \frac{3}{4}

在两边乘以

2

\frac{1}{2} u = - \frac{3}{4}

在两边乘以

2

2 \cdot \frac{1}{2} u = 2 (- \frac{3}{4})

化简

2 \cdot \frac{1}{2} u = 2 (- \frac{3}{4})

化简

2 \cdot \frac{1}{2} u : u

2 \cdot \frac{1}{2} u

分式相乘:

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

= \frac{1 \cdot 2}{2} u

约分:

2

= u \cdot 1

乘以:

u \cdot 1 = u

= u

化简

2 (- \frac{3}{4}) : - \frac{3}{2}

2 (- \frac{3}{4})

去除括号:

(- a) = - a

= - 2 \cdot \frac{3}{4}

分式相乘:

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

= - \frac{3 \cdot 2}{4}

约分:

2

= - \frac{3}{2}

u = - \frac{3}{2}

u = - \frac{3}{2}

u = - \frac{3}{2}

u = sin (x)

代回

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

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

sin (x) = - \frac{3}{2} : x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

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

sin (x) = - \frac{3}{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{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

合并所有解

x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

作图

流行的例子

-2cos^2(θ)+sin(θ)+5=4

- 2 cos^{2} (θ) + sin (θ) + 5 = 4

12 sin^{2} (x) - 9 = 0

2 cos (x - 1) = 0

5 + 6 sin (x) = 0

sin (\frac{π}{2} x) = 0