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受欢迎的三角函数 >

5cos(3x)=-4

解答

5 cos (3 x) = - 4

解答

x = \frac{2.49809 \dots}{3} + \frac{2 πn}{3}, x = - \frac{2.49809 \dots}{3} + \frac{2 πn}{3}

+1

度数

x = 47.71003 \dots^{\circ} + 12 0^{\circ} n, x = - 47.71003 \dots^{\circ} + 12 0^{\circ} n

求解步骤

5 cos (3 x) = - 4

两边除以

5

5 cos (3 x) = - 4

两边除以

5

\frac{5 cos ( 3 x )}{5} = \frac{- 4}{5}

化简

cos (3 x) = - \frac{4}{5}

cos (3 x) = - \frac{4}{5}

使用反三角函数性质

cos (3 x) = - \frac{4}{5}

cos (3 x) = - \frac{4}{5}

的通解

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

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

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

解

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

3 x = arccos (- \frac{4}{5}) + 2 πn

两边除以

3

3 x = arccos (- \frac{4}{5}) + 2 πn

两边除以

3

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

化简

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

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

解

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

3 x = - arccos (- \frac{4}{5}) + 2 πn

两边除以

3

3 x = - arccos (- \frac{4}{5}) + 2 πn

两边除以

3

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

化简

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

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

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

以小数形式表示解

x = \frac{2.49809 \dots}{3} + \frac{2 πn}{3}, x = - \frac{2.49809 \dots}{3} + \frac{2 πn}{3}

作图

流行的例子

sin (2 t) = \frac{7}{9}

sin(2x)+2cos(2x)=0

sin (2 x) + 2 cos (2 x) = 0

cos (x) = \frac{4}{12}

9sin(x)+6cos(x)=10

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