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受欢迎的三角函数 >

-5pisin((pi(t))/2)=7.071

解答

- 5 π sin (\frac{π ( t )}{2}) = 7.071

解答

t = - \frac{2 \cdot 0.46693 \dots}{π} + 4 n, t = 2 + \frac{2 \cdot 0.46693 \dots}{π} + 4 n

+1

度数

t = - 17.03184 \dots^{\circ} + 229.18311 \dots^{\circ} n, t = 131.62340 \dots^{\circ} + 229.18311 \dots^{\circ} n

求解步骤

- 5 π sin (\frac{π ( t )}{2}) = 7.071

两边除以

- 5 π

- 5 π sin (\frac{π t}{2}) = 7.071

两边除以

- 5 π

\frac{- 5 π sin ( \frac{π t}{2} )}{- 5 π} = \frac{7.071}{- 5 π}

化简

\frac{- 5 π sin ( \frac{π t}{2} )}{- 5 π} = \frac{7.071}{- 5 π}

化简

\frac{- 5 π sin ( \frac{π t}{2} )}{- 5 π} : sin (\frac{π t}{2})

\frac{- 5 π sin ( \frac{π t}{2} )}{- 5 π}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

= \frac{5 π sin ( \frac{π t}{2} )}{5 π}

数字相除:

\frac{5}{5} = 1

= \frac{π sin ( \frac{π t}{2} )}{π}

约分:

π

= sin (\frac{π t}{2})

化简

\frac{7.071}{- 5 π} : - 0.45015 \dots

\frac{7.071}{- 5 π}

使用分式法则:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{7.071}{5 π}

化简

\frac{7.071}{5 π} : 0.45015 \dots

\frac{7.071}{5 π}

数字相乘:

5 \cdot 3.14159 \dots = 15.70796 \dots

= \frac{7.071}{15.70796 \dots}

数字相除:

\frac{7.071}{15.70796 \dots} = 0.45015 \dots

= 0.45015 \dots

= - 0.45015 \dots

sin (\frac{π t}{2}) = - 0.45015 \dots

sin (\frac{π t}{2}) = - 0.45015 \dots

sin (\frac{π t}{2}) = - 0.45015 \dots

使用反三角函数性质

sin (\frac{π t}{2}) = - 0.45015 \dots

sin (\frac{π t}{2}) = - 0.45015 \dots

的通解

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

\frac{π t}{2} = arcsin (- 0.45015 \dots) + 2 πn, \frac{π t}{2} = π + arcsin (0.45015 \dots) + 2 πn

\frac{π t}{2} = arcsin (- 0.45015 \dots) + 2 πn, \frac{π t}{2} = π + arcsin (0.45015 \dots) + 2 πn

解

\frac{π t}{2} = arcsin (- 0.45015 \dots) + 2 πn : t = - \frac{2 arcsin ( 0.45015 \dots )}{π} + 4 n

\frac{π t}{2} = arcsin (- 0.45015 \dots) + 2 πn

化简

arcsin (- 0.45015 \dots) + 2 πn : - arcsin (0.45015 \dots) + 2 πn

arcsin (- 0.45015 \dots) + 2 πn

利用以下特性:

arcsin (- x) = - arcsin (x)

arcsin (- 0.45015 \dots) = - arcsin (0.45015 \dots)

= - arcsin (0.45015 \dots) + 2 πn

\frac{π t}{2} = - arcsin (0.45015 \dots) + 2 πn

在两边乘以

2

\frac{π t}{2} = - arcsin (0.45015 \dots) + 2 πn

在两边乘以

2

\frac{2 π t}{2} = - 2 arcsin (0.45015 \dots) + 2 \cdot 2 πn

化简

π t = - 2 arcsin (0.45015 \dots) + 4 πn

π t = - 2 arcsin (0.45015 \dots) + 4 πn

两边除以

π

π t = - 2 arcsin (0.45015 \dots) + 4 πn

两边除以

π

\frac{π t}{π} = - \frac{2 arcsin ( 0.45015 \dots )}{π} + \frac{4 πn}{π}

化简

t = - \frac{2 arcsin ( 0.45015 \dots )}{π} + 4 n

t = - \frac{2 arcsin ( 0.45015 \dots )}{π} + 4 n

解

\frac{π t}{2} = π + arcsin (0.45015 \dots) + 2 πn : t = 2 + \frac{2 arcsin ( 0.45015 \dots )}{π} + 4 n

\frac{π t}{2} = π + arcsin (0.45015 \dots) + 2 πn

在两边乘以

2

\frac{π t}{2} = π + arcsin (0.45015 \dots) + 2 πn

在两边乘以

2

\frac{2 π t}{2} = 2 π + 2 arcsin (0.45015 \dots) + 2 \cdot 2 πn

化简

π t = 2 π + 2 arcsin (0.45015 \dots) + 4 πn

π t = 2 π + 2 arcsin (0.45015 \dots) + 4 πn

两边除以

π

π t = 2 π + 2 arcsin (0.45015 \dots) + 4 πn

两边除以

π

\frac{π t}{π} = \frac{2 π}{π} + \frac{2 arcsin ( 0.45015 \dots )}{π} + \frac{4 πn}{π}

化简

\frac{π t}{π} = \frac{2 π}{π} + \frac{2 arcsin ( 0.45015 \dots )}{π} + \frac{4 πn}{π}

化简

\frac{π t}{π} : t

\frac{π t}{π}

约分:

π

= t

化简

\frac{2 π}{π} + \frac{2 arcsin ( 0.45015 \dots )}{π} + \frac{4 πn}{π} : 2 + \frac{2 arcsin ( 0.45015 \dots )}{π} + 4 n

\frac{2 π}{π} + \frac{2 arcsin ( 0.45015 \dots )}{π} + \frac{4 πn}{π}

消掉

\frac{2 π}{π} : 2

\frac{2 π}{π}

约分:

π

= 2

= 2 + \frac{2 arcsin ( 0.45015 \dots )}{π} + \frac{4 πn}{π}

消掉

\frac{4 πn}{π} : 4 n

\frac{4 πn}{π}

约分:

π

= 4 n

= 2 + \frac{2 arcsin ( 0.45015 \dots )}{π} + 4 n

t = 2 + \frac{2 arcsin ( 0.45015 \dots )}{π} + 4 n

t = 2 + \frac{2 arcsin ( 0.45015 \dots )}{π} + 4 n

t = 2 + \frac{2 arcsin ( 0.45015 \dots )}{π} + 4 n

t = - \frac{2 arcsin ( 0.45015 \dots )}{π} + 4 n, t = 2 + \frac{2 arcsin ( 0.45015 \dots )}{π} + 4 n

以小数形式表示解

t = - \frac{2 \cdot 0.46693 \dots}{π} + 4 n, t = 2 + \frac{2 \cdot 0.46693 \dots}{π} + 4 n

作图

流行的例子

9.8*sin(x)-19.6*cos(x)=4.7

9.8 \cdot sin (x) - 19.6 \cdot cos (x) = 4.7

cos(x)=-sqrt(3)sin(x)

cos (x) = - 3 sin (x)

sin(α)= 3/5 ,0<a< pi/2

sin (α) = \frac{3}{5}, 0 < a < \frac{π}{2}

-(15(0.5cos(x)-sin(x)))/((0.5sin(x)+cos(x))^2)=0

- \frac{15 ( 0.5 cos ( x ) - sin ( x ) )}{( 0.5 sin ( x ) + cos ( x ) ) ^{2}} = 0

solvefor x,0.33=sin(209.42x)

so l v e f or x, 0.33 = sin (209.42 x)