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受欢迎的三角函数 >

7sin(2x)=-2

解答

7 sin (2 x) = - 2

解答

x = - \frac{0.28975 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.28975 \dots}{2} + πn

+1

度数

x = - 8.30077 \dots^{\circ} + 18 0^{\circ} n, x = 98.30077 \dots^{\circ} + 18 0^{\circ} n

求解步骤

7 sin (2 x) = - 2

两边除以

7

7 sin (2 x) = - 2

两边除以

7

\frac{7 sin ( 2 x )}{7} = \frac{- 2}{7}

化简

sin (2 x) = - \frac{2}{7}

sin (2 x) = - \frac{2}{7}

使用反三角函数性质

sin (2 x) = - \frac{2}{7}

sin (2 x) = - \frac{2}{7}

的通解

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

2 x = arcsin (- \frac{2}{7}) + 2 πn, 2 x = π + arcsin (\frac{2}{7}) + 2 πn

2 x = arcsin (- \frac{2}{7}) + 2 πn, 2 x = π + arcsin (\frac{2}{7}) + 2 πn

解

2 x = arcsin (- \frac{2}{7}) + 2 πn : x = - \frac{arcsin ( \frac{2}{7} )}{2} + πn

2 x = arcsin (- \frac{2}{7}) + 2 πn

化简

arcsin (- \frac{2}{7}) + 2 πn : - arcsin (\frac{2}{7}) + 2 πn

arcsin (- \frac{2}{7}) + 2 πn

利用以下特性:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{2}{7}) = - arcsin (\frac{2}{7})

= - arcsin (\frac{2}{7}) + 2 πn

2 x = - arcsin (\frac{2}{7}) + 2 πn

两边除以

2

2 x = - arcsin (\frac{2}{7}) + 2 πn

两边除以

2

\frac{2 x}{2} = - \frac{arcsin ( \frac{2}{7} )}{2} + \frac{2 πn}{2}

化简

x = - \frac{arcsin ( \frac{2}{7} )}{2} + πn

x = - \frac{arcsin ( \frac{2}{7} )}{2} + πn

解

2 x = π + arcsin (\frac{2}{7}) + 2 πn : x = \frac{π}{2} + \frac{arcsin ( \frac{2}{7} )}{2} + πn

2 x = π + arcsin (\frac{2}{7}) + 2 πn

两边除以

2

2 x = π + arcsin (\frac{2}{7}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{π}{2} + \frac{arcsin ( \frac{2}{7} )}{2} + \frac{2 πn}{2}

化简

x = \frac{π}{2} + \frac{arcsin ( \frac{2}{7} )}{2} + πn

x = \frac{π}{2} + \frac{arcsin ( \frac{2}{7} )}{2} + πn

x = - \frac{arcsin ( \frac{2}{7} )}{2} + πn, x = \frac{π}{2} + \frac{arcsin ( \frac{2}{7} )}{2} + πn

以小数形式表示解

x = - \frac{0.28975 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.28975 \dots}{2} + πn

作图

流行的例子

(sin(x)+cos(x))=1

(sin (x) + cos (x)) = 1

sin(θ)=0.72437

sin (θ) = 0.72437

cos (x) = \frac{5}{12}

solvefor a,90=180-2*arccos((2a)/c)

so l v e f or a, 9 0^{\circ} = 18 0^{\circ} - 2 \cdot arccos (\frac{2 a}{c})

cos (x) = \frac{π}{4}