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受欢迎的三角函数 >

2sin(x)+(sqrt(3))/4 = 3/2 ,(0,2pi)

解答

2 sin (x) + \frac{3}{4} = \frac{3}{2}, (0, 2 π)

解答

x = 0.56272 \dots, x = π - 0.56272 \dots

+1

度数

x = 32.24181 \dots^{\circ}, x = 147.75818 \dots^{\circ}

求解步骤

2 sin (x) + \frac{3}{4} = \frac{3}{2}, (0, 2 π)

将

\frac{3}{4}

到右边

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

两边减去

\frac{3}{4}

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

化简

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

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

两边除以

2

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

两边除以

2

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

化简

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

化简

\frac{2 sin ( x )}{2} : sin (x)

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

数字相除:

\frac{2}{2} = 1

= sin (x)

化简

\frac{\frac{3}{2}}{2} - \frac{\frac{3}{4}}{2} : \frac{6 - 3}{8}

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

使用法则

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

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

化简

\frac{3}{2} - \frac{3}{4} : \frac{6 - 3}{4}

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

2, 4

的最小公倍数:

4

2, 4

最小公倍数 (LCM)

2

质因数分解:

2

2

2

是质数，因此无法因数分解

= 2

4

质因数分解:

2 \cdot 2

4

4

除以

24 = 2 \cdot 2

= 2 \cdot 2

将每个因子乘以它在

2

或

4

中出现的最多次数

= 2 \cdot 2

数字相乘:

2 \cdot 2 = 4

= 4

根据最小公倍数调整分式

将每个分子乘以其分母转变为最小公倍数所要乘以的同一数值

4

对于

\frac{3}{2} :

将分母和分子乘以

2

\frac{3}{2} = \frac{3 \cdot 2}{2 \cdot 2} = \frac{6}{4}

= \frac{6}{4} - \frac{3}{4}

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{6 - 3}{4}

= \frac{\frac{6 - 3}{4}}{2}

使用分式法则:

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

= \frac{6 - 3}{4 \cdot 2}

数字相乘:

4 \cdot 2 = 8

= \frac{6 - 3}{8}

sin (x) = \frac{6 - 3}{8}

sin (x) = \frac{6 - 3}{8}

sin (x) = \frac{6 - 3}{8}

使用反三角函数性质

sin (x) = \frac{6 - 3}{8}

sin (x) = \frac{6 - 3}{8}

的通解

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

x = arcsin (\frac{6 - 3}{8}) + 2 πn, x = π - arcsin (\frac{6 - 3}{8}) + 2 πn

x = arcsin (\frac{6 - 3}{8}) + 2 πn, x = π - arcsin (\frac{6 - 3}{8}) + 2 πn

在

(0, 2 π)

范围内的解

x = arcsin (\frac{6 - 3}{8}), x = π - arcsin (\frac{6 - 3}{8})

以小数形式表示解

x = 0.56272 \dots, x = π - 0.56272 \dots

作图

流行的例子

2cos(2x)+sin(x)-4=0

2 cos (2 x) + sin (x) - 4 = 0

- 1 = sec (θ)

(sin(115))/(20)=(sin(b))/(11)

\frac{sin ( 11 5 ^{\circ} )}{20} = \frac{sin ( b )}{11}

cos(θ)=(25)/(sqrt(714))

cos (θ) = \frac{25}{714}

3sec^2(x)-4=0,0<= x<2pi

3 sec^{2} (x) - 4 = 0, 0 \leq x < 2 π