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受欢迎的三角函数 >

2sin(3x)cos(3x)=1

解答

2 sin (3 x) cos (3 x) = 1

解答

x = \frac{π}{12} + \frac{πn}{3}

+1

度数

x = 1 5^{\circ} + 6 0^{\circ} n

求解步骤

2 sin (3 x) cos (3 x) = 1

使用三角恒等式改写

2 sin (3 x) cos (3 x)

使用倍角公式:

2 sin (x) cos (x) = sin (2 x)

= sin (2 \cdot 3 x)

sin (2 \cdot 3 x) = 1

sin (2 \cdot 3 x) = 1

的通解

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

2 \cdot 3 x = \frac{π}{2} + 2 πn

2 \cdot 3 x = \frac{π}{2} + 2 πn

解

2 \cdot 3 x = \frac{π}{2} + 2 πn : x = \frac{π}{12} + \frac{πn}{3}

2 \cdot 3 x = \frac{π}{2} + 2 πn

两边除以

6

2 \cdot 3 x = \frac{π}{2} + 2 πn

两边除以

6

\frac{2 \cdot 3 x}{6} = \frac{\frac{π}{2}}{6} + \frac{2 πn}{6}

化简

\frac{2 \cdot 3 x}{6} = \frac{\frac{π}{2}}{6} + \frac{2 πn}{6}

化简

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

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

数字相乘:

2 \cdot 3 = 6

= \frac{6 x}{6}

数字相除:

\frac{6}{6} = 1

= x

化简

\frac{\frac{π}{2}}{6} + \frac{2 πn}{6} : \frac{π}{12} + \frac{πn}{3}

\frac{\frac{π}{2}}{6} + \frac{2 πn}{6}

\frac{\frac{π}{2}}{6} = \frac{π}{12}

\frac{\frac{π}{2}}{6}

使用分式法则:

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

= \frac{π}{2 \cdot 6}

数字相乘:

2 \cdot 6 = 12

= \frac{π}{12}

\frac{2 πn}{6} = \frac{πn}{3}

\frac{2 πn}{6}

约分:

2

= \frac{πn}{3}

= \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

作图

流行的例子

cos(θ)=sqrt(2)

cos (θ) = 2

6 sin (x) + 15 = 15

sin(x)=1+cos^2(x)

sin (x) = 1 + cos^{2} (x)

cos^2(x)+4cos(x)+1=0

cos^{2} (x) + 4 cos (x) + 1 = 0

arcsin(x)= pi/4

arcsin (x) = \frac{π}{4}