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受欢迎的三角函数 >

6sin(2x)=3cos(30)

解答

6 sin (2 x) = 3 cos (3 0^{\circ})

解答

x = \frac{0.44783 \dots}{2} + 18 0^{\circ} n, x = 9 0^{\circ} - \frac{0.44783 \dots}{2} + 18 0^{\circ} n

+1

弧度

x = \frac{0.44783 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.44783 \dots}{2} + πn

求解步骤

6 sin (2 x) = 3 cos (3 0^{\circ})

cos (3 0^{\circ}) = \frac{3}{2}

cos (3 0^{\circ})

使用以下普通恒等式:

cos (3 0^{\circ}) = \frac{3}{2}

cos (3 0^{\circ})

cos (x)

周期表（周期为

36 0^{\circ} n

）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

= \frac{3}{2}

6 sin (2 x) = 3 \cdot \frac{3}{2}

两边除以

6

6 sin (2 x) = 3 \cdot \frac{3}{2}

两边除以

6

\frac{6 sin ( 2 x )}{6} = \frac{3 \cdot \frac{3}{2}}{6}

化简

\frac{6 sin ( 2 x )}{6} = \frac{3 \cdot \frac{3}{2}}{6}

化简

\frac{6 sin ( 2 x )}{6} : sin (2 x)

\frac{6 sin ( 2 x )}{6}

数字相除:

\frac{6}{6} = 1

= sin (2 x)

化简

\frac{3 \cdot \frac{3}{2}}{6} : \frac{3}{4}

\frac{3 \cdot \frac{3}{2}}{6}

乘

3 \cdot \frac{3}{2} : \frac{3 3}{2}

3 \cdot \frac{3}{2}

分式相乘:

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

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

= \frac{\frac{3 3}{2}}{6}

使用分式法则:

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

= \frac{3 \cdot 3}{2 \cdot 6}

数字相乘:

2 \cdot 6 = 12

= \frac{3 3}{12}

约分:

3

= \frac{3}{4}

sin (2 x) = \frac{3}{4}

sin (2 x) = \frac{3}{4}

sin (2 x) = \frac{3}{4}

使用反三角函数性质

sin (2 x) = \frac{3}{4}

sin (2 x) = \frac{3}{4}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

2 x = arcsin (\frac{3}{4}) + 36 0^{\circ} n, 2 x = 18 0^{\circ} - arcsin (\frac{3}{4}) + 36 0^{\circ} n

2 x = arcsin (\frac{3}{4}) + 36 0^{\circ} n, 2 x = 18 0^{\circ} - arcsin (\frac{3}{4}) + 36 0^{\circ} n

解

2 x = arcsin (\frac{3}{4}) + 36 0^{\circ} n : x = \frac{arcsin ( \frac{3}{4} )}{2} + 18 0^{\circ} n

2 x = arcsin (\frac{3}{4}) + 36 0^{\circ} n

两边除以

2

2 x = arcsin (\frac{3}{4}) + 36 0^{\circ} n

两边除以

2

\frac{2 x}{2} = \frac{arcsin ( \frac{3}{4} )}{2} + \frac{36 0 ^{\circ} n}{2}

化简

x = \frac{arcsin ( \frac{3}{4} )}{2} + 18 0^{\circ} n

x = \frac{arcsin ( \frac{3}{4} )}{2} + 18 0^{\circ} n

解

2 x = 18 0^{\circ} - arcsin (\frac{3}{4}) + 36 0^{\circ} n : x = 9 0^{\circ} - \frac{arcsin ( \frac{3}{4} )}{2} + 18 0^{\circ} n

2 x = 18 0^{\circ} - arcsin (\frac{3}{4}) + 36 0^{\circ} n

两边除以

2

2 x = 18 0^{\circ} - arcsin (\frac{3}{4}) + 36 0^{\circ} n

两边除以

2

\frac{2 x}{2} = 9 0^{\circ} - \frac{arcsin ( \frac{3}{4} )}{2} + \frac{36 0 ^{\circ} n}{2}

化简

x = 9 0^{\circ} - \frac{arcsin ( \frac{3}{4} )}{2} + 18 0^{\circ} n

x = 9 0^{\circ} - \frac{arcsin ( \frac{3}{4} )}{2} + 18 0^{\circ} n

x = \frac{arcsin ( \frac{3}{4} )}{2} + 18 0^{\circ} n, x = 9 0^{\circ} - \frac{arcsin ( \frac{3}{4} )}{2} + 18 0^{\circ} n

以小数形式表示解

x = \frac{0.44783 \dots}{2} + 18 0^{\circ} n, x = 9 0^{\circ} - \frac{0.44783 \dots}{2} + 18 0^{\circ} n

作图

流行的例子

cos (y) = - 1

cot (x) = - \frac{2}{3}

tan((3θ)/4)=(-sqrt(3))/3

tan (\frac{3 θ}{4}) = \frac{- 3}{3}

30=15cos((2pi)/(365)t)+43

30 = 15 cos (\frac{2 π}{365} t) + 43

sin (x) = + 1 e