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受欢迎的三角函数 >

sin^4(x)=sin^4(x)sec(x)

解答

sin^{4} (x) = sin^{4} (x) sec (x)

解答

x = 2 πn, x = π + 2 πn

+1

度数

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

求解步骤

sin^{4} (x) = sin^{4} (x) sec (x)

两边减去

sin^{4} (x) sec (x)

sin^{4} (x) - sin^{4} (x) sec (x) = 0

分解

sin^{4} (x) - sin^{4} (x) sec (x) : - sin^{4} (x) (sec (x) - 1)

sin^{4} (x) - sin^{4} (x) sec (x)

因式分解出通项

- sin^{4} (x)

= - sin^{4} (x) (- 1 + sec (x))

- sin^{4} (x) (sec (x) - 1) = 0

分别求解每个部分

sin^{4} (x) = 0 or sec (x) - 1 = 0

sin^{4} (x) = 0 : x = 2 πn, x = π + 2 πn

sin^{4} (x) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

sin (x) = 0

解是

sin (x) = 0

sin (x) = 0

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}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

解

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

sec (x) - 1 = 0 : x = 2 πn

sec (x) - 1 = 0

将

1

到右边

sec (x) - 1 = 0

两边加上

1

sec (x) - 1 + 1 = 0 + 1

化简

sec (x) = 1

sec (x) = 1

sec (x) = 1

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 = 0 + 2 πn

x = 0 + 2 πn

解

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

合并所有解

x = 2 πn, x = π + 2 πn

作图

流行的例子

cos(x)+sin(x)=2

sin(3θ)cos(θ)-cos(3θ)sin(θ)=(sqrt(3))/2