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受欢迎的三角函数 >

sin(x)*cos(x)= 1/2

解答

sin (x) \cdot cos (x) = \frac{1}{2}

解答

x = \frac{π}{4} + πn

+1

度数

x = 4 5^{\circ} + 18 0^{\circ} n

求解步骤

sin (x) cos (x) = \frac{1}{2}

使用三角恒等式改写

sin (x) cos (x)

使用倍角公式:

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

sin (x) cos (x) = \frac{sin ( 2 x )}{2}

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

\frac{sin ( 2 x )}{2} = \frac{1}{2}

在两边乘以

2

\frac{sin ( 2 x )}{2} = \frac{1}{2}

在两边乘以

2

\frac{2 sin ( 2 x )}{2} = \frac{1 \cdot 2}{2}

化简

\frac{2 sin ( 2 x )}{2} = \frac{1 \cdot 2}{2}

化简

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

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

数字相除:

\frac{2}{2} = 1

= sin (2 x)

化简

\frac{1 \cdot 2}{2} : 1

\frac{1 \cdot 2}{2}

数字相乘:

1 \cdot 2 = 2

= \frac{2}{2}

使用法则

\frac{a}{a} = 1

= 1

sin (2 x) = 1

sin (2 x) = 1

sin (2 x) = 1

sin (2 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 x = \frac{π}{2} + 2 πn

2 x = \frac{π}{2} + 2 πn

解

2 x = \frac{π}{2} + 2 πn : x = \frac{π}{4} + πn

2 x = \frac{π}{2} + 2 πn

两边除以

2

2 x = \frac{π}{2} + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{\frac{π}{2}}{2} + \frac{2 πn}{2}

化简

\frac{2 x}{2} = \frac{\frac{π}{2}}{2} + \frac{2 πn}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{\frac{π}{2}}{2} + \frac{2 πn}{2} : \frac{π}{4} + πn

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

\frac{\frac{π}{2}}{2} = \frac{π}{4}

\frac{\frac{π}{2}}{2}

使用分式法则:

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

= \frac{π}{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= \frac{π}{4}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

= \frac{π}{4} + πn

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

作图

流行的例子

(7sin(2x)+7cos(2x))^2=49

(7 sin (2 x) + 7 cos (2 x))^{2} = 49

-1-tan(x)=sec(x)

- 1 - tan (x) = sec (x)

6tan^2(θ)+10tan(θ)=9tan(θ)+2

6 tan^{2} (θ) + 10 tan (θ) = 9 tan (θ) + 2

2 sin (z) = 1

cos(pi/2-θ)=-sin(θ)

cos (\frac{π}{2} - θ) = - sin (θ)