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受欢迎的三角函数 >

2cos(7x)-sqrt(3)=0

解答

2 cos (7 x) - 3 = 0

解答

x = \frac{π}{42} + \frac{2 πn}{7}, x = \frac{11 π}{42} + \frac{2 πn}{7}

+1

度数

x = 4.28571 \dots^{\circ} + 51.42857 \dots^{\circ} n, x = 47.14285 \dots^{\circ} + 51.42857 \dots^{\circ} n

求解步骤

2 cos (7 x) - 3 = 0

将

3

到右边

2 cos (7 x) - 3 = 0

两边加上

3

2 cos (7 x) - 3 + 3 = 0 + 3

化简

2 cos (7 x) = 3

2 cos (7 x) = 3

两边除以

2

2 cos (7 x) = 3

两边除以

2

\frac{2 cos ( 7 x )}{2} = \frac{3}{2}

化简

cos (7 x) = \frac{3}{2}

cos (7 x) = \frac{3}{2}

cos (7 x) = \frac{3}{2}

的通解

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

7 x = \frac{π}{6} + 2 πn, 7 x = \frac{11 π}{6} + 2 πn

7 x = \frac{π}{6} + 2 πn, 7 x = \frac{11 π}{6} + 2 πn

解

7 x = \frac{π}{6} + 2 πn : x = \frac{π}{42} + \frac{2 πn}{7}

7 x = \frac{π}{6} + 2 πn

两边除以

7

7 x = \frac{π}{6} + 2 πn

两边除以

7

\frac{7 x}{7} = \frac{\frac{π}{6}}{7} + \frac{2 πn}{7}

化简

\frac{7 x}{7} = \frac{\frac{π}{6}}{7} + \frac{2 πn}{7}

化简

\frac{7 x}{7} : x

\frac{7 x}{7}

数字相除:

\frac{7}{7} = 1

= x

化简

\frac{\frac{π}{6}}{7} + \frac{2 πn}{7} : \frac{π}{42} + \frac{2 πn}{7}

\frac{\frac{π}{6}}{7} + \frac{2 πn}{7}

\frac{\frac{π}{6}}{7} = \frac{π}{42}

\frac{\frac{π}{6}}{7}

使用分式法则:

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

= \frac{π}{6 \cdot 7}

数字相乘:

6 \cdot 7 = 42

= \frac{π}{42}

= \frac{π}{42} + \frac{2 πn}{7}

x = \frac{π}{42} + \frac{2 πn}{7}

x = \frac{π}{42} + \frac{2 πn}{7}

x = \frac{π}{42} + \frac{2 πn}{7}

解

7 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{42} + \frac{2 πn}{7}

7 x = \frac{11 π}{6} + 2 πn

两边除以

7

7 x = \frac{11 π}{6} + 2 πn

两边除以

7

\frac{7 x}{7} = \frac{\frac{11 π}{6}}{7} + \frac{2 πn}{7}

化简

\frac{7 x}{7} = \frac{\frac{11 π}{6}}{7} + \frac{2 πn}{7}

化简

\frac{7 x}{7} : x

\frac{7 x}{7}

数字相除:

\frac{7}{7} = 1

= x

化简

\frac{\frac{11 π}{6}}{7} + \frac{2 πn}{7} : \frac{11 π}{42} + \frac{2 πn}{7}

\frac{\frac{11 π}{6}}{7} + \frac{2 πn}{7}

\frac{\frac{11 π}{6}}{7} = \frac{11 π}{42}

\frac{\frac{11 π}{6}}{7}

使用分式法则:

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

= \frac{11 π}{6 \cdot 7}

数字相乘:

6 \cdot 7 = 42

= \frac{11 π}{42}

= \frac{11 π}{42} + \frac{2 πn}{7}

x = \frac{11 π}{42} + \frac{2 πn}{7}

x = \frac{11 π}{42} + \frac{2 πn}{7}

x = \frac{11 π}{42} + \frac{2 πn}{7}

x = \frac{π}{42} + \frac{2 πn}{7}, x = \frac{11 π}{42} + \frac{2 πn}{7}

作图

流行的例子

sec(x)-1=0,0<= x<= 2pi

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(sin(95)}{8.95}=\frac{sin(x))/5

\frac{sin ( 9 5 ^{\circ} )}{8.95} = \frac{sin ( x )}{5}

tan(θ)= 2/(2sqrt(3))

tan (θ) = \frac{2}{2 3}

4 cos (5 x) = 3

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