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受欢迎的三角函数 >

8sec(x)csc(x)=16csc(x)

解答

8 sec (x) csc (x) = 16 csc (x)

解答

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

+1

度数

x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

求解步骤

8 sec (x) csc (x) = 16 csc (x)

两边减去

16 csc (x)

8 sec (x) csc (x) - 16 csc (x) = 0

分解

8 sec (x) csc (x) - 16 csc (x) : 8 csc (x) (sec (x) - 2)

8 sec (x) csc (x) - 16 csc (x)

将

- 16

改写为

2 \cdot 8

= 8 sec (x) csc (x) + 2 \cdot 8 csc (x)

因式分解出通项

8 csc (x)

= 8 csc (x) (sec (x) - 2)

8 csc (x) (sec (x) - 2) = 0

分别求解每个部分

csc (x) = 0 or sec (x) - 2 = 0

csc (x) = 0 :

无解

csc (x) = 0

csc (x) \leq - 1 or csc (x) \geq 1

无解

sec (x) - 2 = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sec (x) - 2 = 0

将

2

到右边

sec (x) - 2 = 0

两边加上

2

sec (x) - 2 + 2 = 0 + 2

化简

sec (x) = 2

sec (x) = 2

sec (x) = 2

的通解

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

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

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

合并所有解

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

作图

流行的例子

sin (2 t) = 0

cos (x) = \frac{1}{6}

sin(2θ)sin(θ)=cos(θ)

sin (2 θ) sin (θ) = cos (θ)

cos^4(2x)= 9/16

cos^{4} (2 x) = \frac{9}{16}

cos(x+pi/4)+cos(x-pi/4)=1

cos (x + \frac{π}{4}) + cos (x - \frac{π}{4}) = 1