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受欢迎的三角函数 >

12csc(x)=3csc(x)+6sqrt(3)

解答

12 csc (x) = 3 csc (x) + 63

解答

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

+1

度数

x = 6 0^{\circ} + 36 0^{\circ} n, x = 12 0^{\circ} + 36 0^{\circ} n

求解步骤

12 csc (x) = 3 csc (x) + 63

用替代法求解

12 csc (x) = 3 csc (x) + 63

令

: csc (x) = u

12 u = 3 u + 63

12 u = 3 u + 63 : u = \frac{2 3}{3}

12 u = 3 u + 63

将

3 u

para o lado esquerdo

12 u = 3 u + 63

两边减去

3 u

12 u - 3 u = 3 u + 63 - 3 u

化简

9 u = 63

9 u = 63

两边除以

9

9 u = 63

两边除以

9

\frac{9 u}{9} = \frac{6 3}{9}

化简

u = \frac{2 3}{3}

u = \frac{2 3}{3}

u = csc (x)

代回

csc (x) = \frac{2 3}{3}

csc (x) = \frac{2 3}{3}

csc (x) = \frac{2 3}{3} : x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

csc (x) = \frac{2 3}{3}

csc (x) = \frac{2 3}{3}

的通解

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

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

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

合并所有解

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

作图

流行的例子

2-2csc^2(x)=-csc^2(x)+csc(x)

2 - 2 csc^{2} (x) = - csc^{2} (x) + csc (x)

4 cot (x) + 5 = 1

1/36+cos^2(θ)=1

\frac{1}{36} + cos^{2} (θ) = 1

2sin(x)-(2+sqrt(2))=-sqrt(2)csc(x)

2 sin (x) - (2 + 2) = - 2 csc (x)

5cos(A)-sqrt(10)=0

5 cos (A) - 10 = 0