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受欢迎的三角函数 >

7.5=5sin(pi/2 (x-2))+5

解答

7.5 = 5 sin (\frac{π}{2} (x - 2)) + 5

解答

x = 4 n + \frac{7}{3}, x = 4 n + \frac{11}{3}

+1

度数

x = 133.69015 \dots^{\circ} + 229.18311 \dots^{\circ} n, x = 210.08452 \dots^{\circ} + 229.18311 \dots^{\circ} n

求解步骤

7.5 = 5 sin (\frac{π}{2} (x - 2)) + 5

交换两边

5 sin (\frac{π}{2} (x - 2)) + 5 = 7.5

将

5

到右边

5 sin (\frac{π}{2} (x - 2)) + 5 = 7.5

两边减去

5

5 sin (\frac{π}{2} (x - 2)) + 5 - 5 = 7.5 - 5

化简

5 sin (\frac{π}{2} (x - 2)) = 2.5

5 sin (\frac{π}{2} (x - 2)) = 2.5

两边除以

5

5 sin (\frac{π}{2} (x - 2)) = 2.5

两边除以

5

\frac{5 sin ( \frac{π}{2} ( x - 2 ) )}{5} = \frac{2.5}{5}

化简

sin (\frac{π}{2} (x - 2)) = 0.5

sin (\frac{π}{2} (x - 2)) = 0.5

sin (\frac{π}{2} (x - 2)) = 0.5

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}

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

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

解

\frac{π}{2} (x - 2) = \frac{π}{6} + 2 πn : x = 4 n + \frac{7}{3}

\frac{π}{2} (x - 2) = \frac{π}{6} + 2 πn

在两边乘以

2

\frac{π}{2} (x - 2) = \frac{π}{6} + 2 πn

在两边乘以

2

2 \cdot \frac{π}{2} (x - 2) = 2 \cdot \frac{π}{6} + 2 \cdot 2 πn

化简

2 \cdot \frac{π}{2} (x - 2) = 2 \cdot \frac{π}{6} + 2 \cdot 2 πn

化简

2 \cdot \frac{π}{2} (x - 2) : π (x - 2)

2 \cdot \frac{π}{2} (x - 2)

分式相乘:

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

= \frac{2 π}{2} (x - 2)

约分:

2

= (x - 2) π

化简

2 \cdot \frac{π}{6} + 2 \cdot 2 πn : \frac{π}{3} + 4 πn

2 \cdot \frac{π}{6} + 2 \cdot 2 πn

2 \cdot \frac{π}{6} = \frac{π}{3}

2 \cdot \frac{π}{6}

分式相乘:

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

= \frac{π 2}{6}

约分:

2

= \frac{π}{3}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

数字相乘:

2 \cdot 2 = 4

= 4 πn

= \frac{π}{3} + 4 πn

π (x - 2) = \frac{π}{3} + 4 πn

π (x - 2) = \frac{π}{3} + 4 πn

π (x - 2) = \frac{π}{3} + 4 πn

两边除以

π

π (x - 2) = \frac{π}{3} + 4 πn

两边除以

π

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

化简

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

化简

\frac{π ( x - 2 )}{π} : x - 2

\frac{π ( x - 2 )}{π}

约分:

π

= x - 2

化简

\frac{\frac{π}{3}}{π} + \frac{4 πn}{π} : \frac{1}{3} + 4 n

\frac{\frac{π}{3}}{π} + \frac{4 πn}{π}

\frac{\frac{π}{3}}{π} = \frac{1}{3}

\frac{\frac{π}{3}}{π}

使用分式法则:

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

= \frac{π}{3 π}

约分:

π

= \frac{1}{3}

\frac{4 πn}{π} = 4 n

\frac{4 πn}{π}

约分:

π

= 4 n

= \frac{1}{3} + 4 n

x - 2 = \frac{1}{3} + 4 n

x - 2 = \frac{1}{3} + 4 n

x - 2 = \frac{1}{3} + 4 n

将

2

到右边

x - 2 = \frac{1}{3} + 4 n

两边加上

2

x - 2 + 2 = \frac{1}{3} + 4 n + 2

化简

x - 2 + 2 = \frac{1}{3} + 4 n + 2

化简

x - 2 + 2 : x

x - 2 + 2

同类项相加:

- 2 + 2 = 0

= x

化简

\frac{1}{3} + 4 n + 2 : 4 n + \frac{7}{3}

\frac{1}{3} + 4 n + 2

合并分式

2 + \frac{1}{3} : \frac{7}{3}

2 + \frac{1}{3}

将项转换为分式:

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

= \frac{2 \cdot 3}{3} + \frac{1}{3}

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 3 + 1}{3}

2 \cdot 3 + 1 = 7

2 \cdot 3 + 1

数字相乘:

2 \cdot 3 = 6

= 6 + 1

数字相加:

6 + 1 = 7

= 7

= \frac{7}{3}

= 4 n + \frac{7}{3}

x = 4 n + \frac{7}{3}

x = 4 n + \frac{7}{3}

x = 4 n + \frac{7}{3}

解

\frac{π}{2} (x - 2) = \frac{5 π}{6} + 2 πn : x = 4 n + \frac{11}{3}

\frac{π}{2} (x - 2) = \frac{5 π}{6} + 2 πn

在两边乘以

2

\frac{π}{2} (x - 2) = \frac{5 π}{6} + 2 πn

在两边乘以

2

2 \cdot \frac{π}{2} (x - 2) = 2 \cdot \frac{5 π}{6} + 2 \cdot 2 πn

化简

2 \cdot \frac{π}{2} (x - 2) = 2 \cdot \frac{5 π}{6} + 2 \cdot 2 πn

化简

2 \cdot \frac{π}{2} (x - 2) : π (x - 2)

2 \cdot \frac{π}{2} (x - 2)

分式相乘:

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

= \frac{2 π}{2} (x - 2)

约分:

2

= (x - 2) π

化简

2 \cdot \frac{5 π}{6} + 2 \cdot 2 πn : \frac{5 π}{3} + 4 πn

2 \cdot \frac{5 π}{6} + 2 \cdot 2 πn

2 \cdot \frac{5 π}{6} = \frac{5 π}{3}

2 \cdot \frac{5 π}{6}

分式相乘:

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

= \frac{5 π 2}{6}

数字相乘:

5 \cdot 2 = 10

= \frac{10 π}{6}

约分:

2

= \frac{5 π}{3}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

数字相乘:

2 \cdot 2 = 4

= 4 πn

= \frac{5 π}{3} + 4 πn

π (x - 2) = \frac{5 π}{3} + 4 πn

π (x - 2) = \frac{5 π}{3} + 4 πn

π (x - 2) = \frac{5 π}{3} + 4 πn

两边除以

π

π (x - 2) = \frac{5 π}{3} + 4 πn

两边除以

π

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

化简

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

化简

\frac{π ( x - 2 )}{π} : x - 2

\frac{π ( x - 2 )}{π}

约分:

π

= x - 2

化简

\frac{\frac{5 π}{3}}{π} + \frac{4 πn}{π} : \frac{5}{3} + 4 n

\frac{\frac{5 π}{3}}{π} + \frac{4 πn}{π}

\frac{\frac{5 π}{3}}{π} = \frac{5}{3}

\frac{\frac{5 π}{3}}{π}

使用分式法则:

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

= \frac{5 π}{3 π}

约分:

π

= \frac{5}{3}

\frac{4 πn}{π} = 4 n

\frac{4 πn}{π}

约分:

π

= 4 n

= \frac{5}{3} + 4 n

x - 2 = \frac{5}{3} + 4 n

x - 2 = \frac{5}{3} + 4 n

x - 2 = \frac{5}{3} + 4 n

将

2

到右边

x - 2 = \frac{5}{3} + 4 n

两边加上

2

x - 2 + 2 = \frac{5}{3} + 4 n + 2

化简

x - 2 + 2 = \frac{5}{3} + 4 n + 2

化简

x - 2 + 2 : x

x - 2 + 2

同类项相加:

- 2 + 2 = 0

= x

化简

\frac{5}{3} + 4 n + 2 : 4 n + \frac{11}{3}

\frac{5}{3} + 4 n + 2

合并分式

2 + \frac{5}{3} : \frac{11}{3}

2 + \frac{5}{3}

将项转换为分式:

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

= \frac{2 \cdot 3}{3} + \frac{5}{3}

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 3 + 5}{3}

2 \cdot 3 + 5 = 11

2 \cdot 3 + 5

数字相乘:

2 \cdot 3 = 6

= 6 + 5

数字相加:

6 + 5 = 11

= 11

= \frac{11}{3}

= 4 n + \frac{11}{3}

x = 4 n + \frac{11}{3}

x = 4 n + \frac{11}{3}

x = 4 n + \frac{11}{3}

x = 4 n + \frac{7}{3}, x = 4 n + \frac{11}{3}

作图

流行的例子

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2 cos (θ) + 23 = 3

-2sqrt(2)=-4sin(2θ)

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8 cos (x) = 4 cos^{2} (x) + 3

(26)/(sin(88))=(21)/(sin(c))

\frac{26}{sin ( 8 8 ^{\circ} )} = \frac{21}{sin ( c )}

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