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受欢迎的三角函数 >

960=480(1-cos(7.5x))

解答

960 = 480 (1 - cos (7.5 x))

解答

x = \frac{2 π}{15} + \frac{4 πn}{15}

+1

度数

x = 2 4^{\circ} + 4 8^{\circ} n

求解步骤

960 = 480 (1 - cos (7.5 x))

交换两边

480 (1 - cos (7.5 x)) = 960

两边除以

480

480 (1 - cos (7.5 x)) = 960

两边除以

480

\frac{480 ( 1 - cos ( 7.5 x ) )}{480} = \frac{960}{480}

化简

1 - cos (7.5 x) = 2

1 - cos (7.5 x) = 2

将

1

到右边

1 - cos (7.5 x) = 2

两边减去

1

1 - cos (7.5 x) - 1 = 2 - 1

化简

- cos (7.5 x) = 1

- cos (7.5 x) = 1

两边除以

- 1

- cos (7.5 x) = 1

两边除以

- 1

\frac{- cos ( 7.5 x )}{- 1} = \frac{1}{- 1}

化简

cos (7.5 x) = - 1

cos (7.5 x) = - 1

cos (7.5 x) = - 1

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}

7.5 x = π + 2 πn

7.5 x = π + 2 πn

解

7.5 x = π + 2 πn : x = \frac{2 π}{15} + \frac{4 πn}{15}

7.5 x = π + 2 πn

在两边乘以

10

7.5 x = π + 2 πn

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

7.5 x \cdot 10 = π 10 + 2 πn \cdot 10

整理后得

75 x = 10 π + 20 πn

75 x = 10 π + 20 πn

两边除以

75

75 x = 10 π + 20 πn

两边除以

75

\frac{75 x}{75} = \frac{10 π}{75} + \frac{20 πn}{75}

化简

\frac{75 x}{75} = \frac{10 π}{75} + \frac{20 πn}{75}

化简

\frac{75 x}{75} : x

\frac{75 x}{75}

数字相除:

\frac{75}{75} = 1

= x

化简

\frac{10 π}{75} + \frac{20 πn}{75} : \frac{2 π}{15} + \frac{4 πn}{15}

\frac{10 π}{75} + \frac{20 πn}{75}

消掉

\frac{10 π}{75} : \frac{2 π}{15}

\frac{10 π}{75}

约分:

5

= \frac{2 π}{15}

= \frac{2 π}{15} + \frac{20 πn}{75}

消掉

\frac{20 πn}{75} : \frac{4 πn}{15}

\frac{20 πn}{75}

约分:

5

= \frac{4 πn}{15}

= \frac{2 π}{15} + \frac{4 πn}{15}

x = \frac{2 π}{15} + \frac{4 πn}{15}

x = \frac{2 π}{15} + \frac{4 πn}{15}

x = \frac{2 π}{15} + \frac{4 πn}{15}

x = \frac{2 π}{15} + \frac{4 πn}{15}

作图

流行的例子

8 = 8 tan (θ)

2sin(2x)-3cos(x)=0

2 sin (2 x) - 3 cos (x) = 0

4cos(θ)=2cos(θ)

4 cos (θ) = 2 cos (θ)

2 cos (θ) = - 2

solvefor x,cos(2x)+2/(cos(2x))+3=0

so l v e f or x, cos (2 x) + \frac{2}{cos ( 2 x )} + 3 = 0