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受欢迎的三角函数 >

3cot(x)+1=2+4cot(x),0<= x<= 360

解答

3 cot (x) + 1 = 2 + 4 cot (x), 0^{\circ} \leq x \leq 36 0^{\circ}

解答

x = 13 5^{\circ}, x = 31 5^{\circ}

+1

弧度

x = \frac{3 π}{4}, x = \frac{7 π}{4}

求解步骤

3 cot (x) + 1 = 2 + 4 cot (x), 0^{\circ} \leq x \leq 36 0^{\circ}

用替代法求解

3 cot (x) + 1 = 2 + 4 cot (x)

令

: cot (x) = u

3 u + 1 = 2 + 4 u

3 u + 1 = 2 + 4 u : u = - 1

3 u + 1 = 2 + 4 u

将

1

到右边

3 u + 1 = 2 + 4 u

两边减去

1

3 u + 1 - 1 = 2 + 4 u - 1

化简

3 u = 4 u + 1

3 u = 4 u + 1

将

4 u

para o lado esquerdo

3 u = 4 u + 1

两边减去

4 u

3 u - 4 u = 4 u + 1 - 4 u

化简

- u = 1

- u = 1

两边除以

- 1

- u = 1

两边除以

- 1

\frac{- u}{- 1} = \frac{1}{- 1}

化简

u = - 1

u = - 1

u = cot (x)

代回

cot (x) = - 1

cot (x) = - 1

cot (x) = - 1, 0 \leq x \leq 36 0^{\circ} : x = 13 5^{\circ}, x = 31 5^{\circ}

cot (x) = - 1, 0 \leq x \leq 36 0^{\circ}

cot (x) = - 1

的通解

cot (x)

周期表（周期为

18 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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = 13 5^{\circ} + 18 0^{\circ} n

x = 13 5^{\circ} + 18 0^{\circ} n

在

0 \leq x \leq 36 0^{\circ}

范围内的解

x = 13 5^{\circ}, x = 31 5^{\circ}

合并所有解

x = 13 5^{\circ}, x = 31 5^{\circ}

作图

流行的例子

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sin (x) = \frac{48.35}{50.14}

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1.47 = (\frac{sin ( \frac{x + 60}{2} )}{sin ( 3 0 ^{\circ} )})

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