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受欢迎的三角函数 >

3csc(x)=4+csc(x)

解答

3 csc (x) = 4 + csc (x)

解答

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

+1

度数

x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n

求解步骤

3 csc (x) = 4 + csc (x)

用替代法求解

3 csc (x) = 4 + csc (x)

令

: csc (x) = u

3 u = 4 + u

3 u = 4 + u : u = 2

3 u = 4 + u

将

u

para o lado esquerdo

3 u = 4 + u

两边减去

u

3 u - u = 4 + u - u

化简

2 u = 4

2 u = 4

两边除以

2

2 u = 4

两边除以

2

\frac{2 u}{2} = \frac{4}{2}

化简

u = 2

u = 2

u = csc (x)

代回

csc (x) = 2

csc (x) = 2

csc (x) = 2 : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

csc (x) = 2

csc (x) = 2

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}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

合并所有解

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

作图

流行的例子

tan (θ) = - \frac{8}{15}

4 cos (t) = 0

7sec^3(x)+16sec^2(x)+11sec(x)+2=0

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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})