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受欢迎的三角函数 >

1+sin(5x)=0

解答

1 + sin (5 x) = 0

解答

x = \frac{3 π}{10} + \frac{2 πn}{5}

+1

度数

x = 5 4^{\circ} + 7 2^{\circ} n

求解步骤

1 + sin (5 x) = 0

将

1

到右边

1 + sin (5 x) = 0

两边减去

1

1 + sin (5 x) - 1 = 0 - 1

化简

sin (5 x) = - 1

sin (5 x) = - 1

sin (5 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}

5 x = \frac{3 π}{2} + 2 πn

5 x = \frac{3 π}{2} + 2 πn

解

5 x = \frac{3 π}{2} + 2 πn : x = \frac{3 π}{10} + \frac{2 πn}{5}

5 x = \frac{3 π}{2} + 2 πn

两边除以

5

5 x = \frac{3 π}{2} + 2 πn

两边除以

5

\frac{5 x}{5} = \frac{\frac{3 π}{2}}{5} + \frac{2 πn}{5}

化简

\frac{5 x}{5} = \frac{\frac{3 π}{2}}{5} + \frac{2 πn}{5}

化简

\frac{5 x}{5} : x

\frac{5 x}{5}

数字相除:

\frac{5}{5} = 1

= x

化简

\frac{\frac{3 π}{2}}{5} + \frac{2 πn}{5} : \frac{3 π}{10} + \frac{2 πn}{5}

\frac{\frac{3 π}{2}}{5} + \frac{2 πn}{5}

\frac{\frac{3 π}{2}}{5} = \frac{3 π}{10}

\frac{\frac{3 π}{2}}{5}

使用分式法则:

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

= \frac{3 π}{2 \cdot 5}

数字相乘:

2 \cdot 5 = 10

= \frac{3 π}{10}

= \frac{3 π}{10} + \frac{2 πn}{5}

x = \frac{3 π}{10} + \frac{2 πn}{5}

x = \frac{3 π}{10} + \frac{2 πn}{5}

x = \frac{3 π}{10} + \frac{2 πn}{5}

x = \frac{3 π}{10} + \frac{2 πn}{5}

作图

流行的例子

0= pi/2-2arctan((pi/2-2-c)/(pi/2-c))

0 = \frac{π}{2} - 2 arctan (\frac{\frac{π}{2} - 2 - c}{\frac{π}{2} - c})

2sin(2x+10)-sqrt(3)=0

2 sin (2 x + 10) - 3 = 0

cos(θ)=(13)/(sqrt(6)*\sqrt{86)}

cos (θ) = \frac{13}{6 \cdot 86}

(1+tan(x))/(1+cot(x))=2

\frac{1 + tan ( x )}{1 + cot ( x )} = 2

tan(x)+1= 1/(sqrt(3))+1/(sqrt(3))cot(x)

tan (x) + 1 = \frac{1}{3} + \frac{1}{3} cot (x)